Adon
Birdie
Eagle
You'll be pleased to learn that Lee is one of Eagle's worst matchups. Your damage is about even and you can shut him down if you play your cards right. Don't think it's a free matchup, however; Eagle's a strong, volatile character that can easily take the game if you let your guard down. Stay aware and keep him in check.
Your best course of action is to stay at least halfscreen from Eagle. Depending on the other player's plan, they might try to go aggressive, or stay out of your HP range and turtle. HP is great in this matchup but should be used carefully. If you're throwing HP out predictably, the Eagle can punish you hard with moves like HP, that can potentially do up to 50% of your health. If used unpredictably, however, it's a great tool to condition Eagle and make them respect you more.
MK is fantastic against Eagle. He struggles to contest it well due to the crouching and long range, also giving you time to approach on hit. Use it.
Jumpkick's strong to close a life deficit gap if necessary; it's also surprisingly clean when it comes to air to air provided it's done early enough. Eagle's going to be looking out for it, however. Make sure the Eagle's unaware before throwing it out or you'll eat a heavy anti air.
One important, but not necessarily easy, thing you'll have to maintain is remaining proper distance from Eagle. Lee's terrible up-close options make it so if you get cornered you likely won't get out. Jump back when needed, do not get too overzealous with jump attacks or HPs. If you're close after a jumpin, jump back or MK. If you manage to corner Eagle, play it safe and play at the tip of your MK range, but don't get too fixated on keeping the corner.
Watch out for Eagle's jump; it'll go over all your attacks and can screw you up if you aren't spacing yourself to deal with it. The most consistent option if he jumps from far away is to punish his landing with an MK. If he's closer and tries to jump, try to go under him with walking or HP to maintain spacing. MP and HK can situationally work as anti airs, but be aware of the ranges and timings where they'll work, because if the anti air backfires, it'll hurt.
Videos of the matchup:
https://www.youtube.com/watch?v=JsQ3LVb1wnQ
https://www.youtube.com/watch?v=LeF6v6QzAJc
Geki
Gen
The fight versus Gen is a surprisingly even one. Lee's HP is one of the best counters to Gen's scissor kick (MK/HK) in the game due to its range and damage. Learning to react to the opponent's scissor kick or being able to predict when they'll use it is incredibly powerful for a safe approach. Jumpkick is another great means of approaching him, but if done too predictably, he can block it and counter for big damage. Cool off on the jumpkicks if the opponent has a read on you.
The biggest struggle against Gen will likely be dealing with his own jumpkick. Lee doesn't have a particularly strong set of anti-airs, so you may struggle to find a consistent counter to jumpkick-heavy Gen play. The best answer is if you're expecting a jumpkick from Gen, do a jumpkick yourself. Lee jumps a fair bit higher than Gen, and over his jumpkick hitbox, so Lee can contest him in air-to-air quite well. There's no way to anti-air Gen on reaction, unfortunately, so this is your best bet.
The dynamic of the match can shift pretty heavily depending on what your opponent is doing, so be sure to keep an eye out for the tools they're using and decisions. For example, Lee can get away with being quite aggressive in this matchup, but not if the Gen is fishing for a block. If he's doing that, then it's best to wait him out with fake outs until he lets his guard down.
A video of the matchup can be found here: https://www.youtube.com/watch?v=ZG-x8UGw1Uk
Lee
Joe
Mike
This matchup is very much in Lee's favor, primarily due to MK blocking out Mike's approach most of the time. Use a lot of it! Honestly, for the most part, that's kind of it. Use a lot of MK to keep him away (but don't get too careless). You can try getting a surprise attack with HP, but it's very risky and might not be worth it.
Retsu
Retsu is a favorable matchup for Lee. HP is a rock-solid counter to Retsu's infamous HK. You may have trouble with Retsu's jumpkick more than anything else, but with omniblock -> LP you can anti air it with solid reactions. Tread carefully against more aggressive Retsu players. MK is a solid option up close, since it ducks/outpokes most of his moves. If you play reactively and carefully, you should be able to beat almost any Retsu that comes your way.
