A while ago, I saw a request on reddit asking for a list of all early or late game champions, so I'm going to go into detail about why I categorize each as I did.

For reference

Early Game: The laning levels, mainly the first 15 or 20 minutes, when it is most likely just between you and your lane opponent. Levels 1-9

Mid Game: After the laning phase. This is when you see more roaming occur, and the first towers should start to fall. One team generally has a clear advantage by this point. Levels 9-16

Late game: After about 30 or 40 minutes. This is when the carries start to get their fifth or sixth items and live up to their names. This is when death timers are high and one team fight can lead to disaster for one team. Levels 16+

Part 1 can be found here.

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Janna: Mid Game (Support and AP). Janna is known for her CC, her shield, and her potentially game changing ultimate. Her shield is incredibly strong from level 9 on, giving her target 50 additional attack damage, and a rather hefty shield. She has great Crowd Control with her Q and Ultimate, but late game her shield is kind of neglible, and if you want a support that helps your AD do extra damage, Nunu is a better choice, also is naturally squishy, but strong mid game due to CC. when built fully AP, she has strong poke and good range, but shes incredibly squishy and lacks the damage of other mages.

Jarvan IV: Early/Mid Game. Has a great jungle clear time thanks to his passive, and his ganks are terrifying if you can land an e>q combination. Falls off a bit due to his W being a terrible ability without scaling, but his Ultimate can be great at potentially zoning a carry.

Jax: Late Game. Jax has an alright laning phase, and can farm well under tower thanks to his W, and his E gives him very solid utility. Late game though, as he builds damage, he becomes one of the best duelists in the game, and scales very well. His largest drawbacks is being focused down potentially, but he has great mobility and a very unique dodge ability, and is great at snowballing a game, largest drawback is being shut down early game.

Jayce: Mid/Late Game. Thanks to his ability to transfer between ranged and melee, Jayce has a decent early game in the top lane, able to harass and farm from relatively safety, and have a good follow up with his hammer form. Jayce really seems to shine mid game with his poke from his Q and E. Bloodthirster/Manamura Jayce, which has recently grown in popularity, scales better into late game and works as almost a second AD carry for your team, but Jayce bruiser works better late game with still solid poke.

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Karma: Late Game (AP). Right now, Karma has the lowest win rate in the entire game, being beaten out by even Olaf or Viktor, but has buffs coming into the next patch, so maybe Karma will have the tools needed to be a viable pick. as for her right now, Karma has good range and extremely good initiation, as her E is a very good ability. However, her damage is reliant on her Q, which is a skillshot, and her W, which is a leash into root, similar to leblancs, but much worse mechanically. However, her E is great initiation and should not be underestimated, and is great with the mantra shield burst.

Support: Early Game. Most people agree Karma support is useless, but it does have a place. Karma suupport has good bush control with her Q, and her E is good for letting junglers gank with the speed boost. However, she needs damage to remain relevant, and its hard to get that as a support, resulting in her falling off.

Karthus: Late Game. In laning phase and early game, the only thing that Karthus counters in lane is minions. However, he does this very well, and he is one of the best farmers in the game. As the game draws on, as Karthus gets more items, he becomes ever more powerful, and he has great AP scaling, huge AOE damage, and a devastating ultimate.

Kassadin: Mid Game. Kassadin has a weak 1-5, as his melee range makes him susceptible to harassment from other mid laners. However, as soon as he hits 6, Kassadin has great burst potential, and huge roaming potential. This makes him incredibly deadly, and gives him huge map pressure. His short range does hurt him as the game drags on and AD carries become more powerful, but he still does ridiculous amounts of damage and has great pushing power.

Katarina: Mid Game. Very similar to Kassadin in her early game, but post 6 she has lots of burst potential, and has an awesome AOE teamfight. Falls of late game due to vulnerability to Crowd Control and can potentially be kited unless she has a team that can dive into the enemy along with her.

Kayle: AD: Early/Mid Game. Popularized by Dyrus at 2011 MLG Anaheim, AD Kayle is one of the best lane bullies in the game, though has fallen off lately, especially with her Q no longer granting damage amplification. However, Kayle, with her E and Q scaling off of AD, is a great lane bully against melee champions, and was one of the best counters to shen before his nerfs. Never really falls off, and has an incredible ultimate, but doesn't scale as well as AP, and without CDR, will be forced into awkward melee at times.
AP: Late Game. AP Kayle is ridiculously strong, drawing the most bans out of all champions in LCS. Her Q and E both have solid AP scaling, and has a decent heal and a great utility ultimate. However, shes received a string of nerfs lately, along with Nashors Tooth being nerfed, a key item on her. Has great damage and utility late game.

Kennen AD: Early Game. With his W boosting his every fifth autoattack, AD Kennen has great harass early, and is incredibly annoying to have to deal with, and he has a reliable stun with his ultimate, and an escape with his e. However, none of his abilities actually scale with AD, so he falls off late game with his abilities, and other AD carries are a better choice.

Kennen AP: Mid/Late Game. Has an alright laning phase, benefits a lot with AD runes for harass and last hitting. However, with AP items, Kennen has a very solid teamfight thanks to his ultimate. However, he is completely reliant on his ultimate, and is rather useless without it, but can stun pretty much the entire enemy team with great damage.

Kha'Zix: Mid Game. Doesn't really shine in the laning phase, but has great harass and farm at level 6 with his evolved void spikes. From level 11 onward, he has a great team fight with his evolved wings, letting him get resets and have huge mobility. Doesn't really have a falling off point, but can get burst down if he builds straight damage, and he doesn't mix well with lots of defensive items.

Kog'Maw: Late Game. With his W dealing % health and granting him range, and passive attack speed on his Q, he has huge scaling into late game, and is really only outclassed by Tristana. However, he doesn't have a good early game, as he has no natural escapes, making him vulnerable to ganks, and reliable on summoner spells.

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Le'blanc: Early Game. Has one of the best laning phases in the game, with huge burst on Q and R, and a silence that makes her impossible to trade with, with a strong utility root. However, he AP scaling and farming is rather terrible compared to most mages, so falls off rather hard late game, although if she can get to the AD carry throughout all times of the game, he will die.

Lee Sin: Early Game. With a recent string of nerfs, Lee Sin is one of the most mechanically difficult champions in the game, but with a lot of damage nerfs lately, it isn't really worth that risk. His mobility and his ganks are devestating early, but late game, he can be burst down if building damage, and if building tanky, doesn't deal enough damage to be a threat.

Leona: All Game. Leona is a CC and aura bot, and thats how she should be played. Has a good early game if paired with an agressive ADC, and her teamfighting with her ultimate is excellent. However, she is vulnerable to being kited, and can be burst down quickly if she doesn't have defensive items yet, as she has to dive into the enemy team to be effective.

Lissandra: Mid Game. Lissandra is in pretty bad needs of buffs, and in Riot's continuing cycle of releasing champions as either overpowered or underpowered, Lissandra fell on the underpowered side. She has a decent laning phase, but with her teamfighting, she has to get to close to the enemies to deal damage. Hopefully her self-ult duration buff will help her, but she might need more.

Lulu: Support: Early/Mid Game: Lulu is a champion with excellent poke and bush control as a support, mainly through maxing Q. Likewise, her polymorph ability is one of the best disables in the game, a blind and silence rolled into one, and her ultimate is a unique ability that coordinates very well with a champion that will plan on diving into the enemy team thanks to the knock up and slow.

AP: Mid Game. Like support Lulu, has great damage early, along with great brush control. As the game scales later, Lulu's decent AP scaling and great utility make her an awesome protect the carry, and her AP ultimate will give the target a huge amount of health. Doesn't have that much damage late game compared to other APs.

Lux: Mid/Late Game. Lux's laning phase focuses on farming, and all throughout the early game, she doesn't deal that much damage. However, once she has either an Athene's or morellonomicon and a deathcap, she gets a huge spike in power with AP and CDR. It is generally at this point where Lux can start catching people out, and one shotting people, or a whole team. Lux has huge burst, and great AP scaling, and the cooldown on her ultimate is very short, even with the nerf coming out.

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Malphite: Late Game. Doesn't have a very strong laning phase, and can actually get bullied pretty easily. However, as soon as Malphite is able to get some armor and health, he becomes an unstoppable force, and his ultimate really IS an unstoppable force, and is devestating in teamfights, and probably the best initiation in the game, if you have a team following you up.

Malzahar: Mid Game. To be honest, you probably shouldn't really be playing Malzahar. He doesn't have a stellar laning phase, he has good poke and harass, but very low mobility. His Ultimate is very strong, but leaves you completely vulnerable to the enemy team's burst, and a quicksilver sash is a hard counter.

Makoi: Early and Late Game. This seems odd. However, Makoi has very reliable CC and his ganks are deadly as a result, giving him good pressure on the map, although his clear speed can be a bit lacking. However, after a while, his CC falls off, but its his ultimate, when ranked up a couple of times, that gives him huge amounts of utility and is invaluable for any team, reducing incoming damage for his entire team.

Master Yi AP: Mid Game. AP Master Yi, generally played in the mid lane, relies on resets in team fights and cleaning up using his Q and a lich bane. However, Yi's damage needs AP to get to the point where it can deal enough damage to be a threat, but as the game gets later, his lack of reliable damage and vulnerability to CC makes him less threatening.

AD: Late Game. Master Yi is kind of an odd champion, but as shown by Crumbzz during a few memorable moments on his stream, the backdooring potential of AD Master Yi is absolutely ridiculous. Thanks to his heal, which recently had its base heal buffed, and an incredibly infuriating ultimate which makes him immune to slows, AD Master Yi can build straight damage, and with his Wuju Stye buff and a good gap closer, he can deal gigantic damage.

Miss Fortune: Early/Mid Game. Miss fortune, simply put, is a huge lane bully. Her double up Q and impure shots make for great harassment, and she can easily get a control of a lane, leading to early domination. As she scales into mid game, her lack of a good steroid and escape make her not as good as other ADCs, but her ultimate deals huge AOE damage, and when used in cunjuction with a team, is incredibly terrifying. She falls off late game compared to other ADCs in terms of damage.

Mordekaiser: Late Game. Similar to Karthus, Mordekaiser counters minions better than anyone else, and is one of the best farmers in teh gaem with massive AOE damage. As he scales into late game, his ultimate against an enemy ADC makes him terrifying against a back line, and lets him deal massive damage onto the enemy team.

Morgana: Mid Game. Early game, Morgana doesn't put much pressure onto the map, if any. However, she has a great teamfight presence, especially with Zhonya's Hourglass, and her Q makes her great for sieging a tower. She falls off late game though, as she doesn't have much damage outside her ultimate, and she gets outclassed by other champions.

Thanks for reading guys, and please wait for the next installment in this incredibly long series. Good luck on the fields of justice!