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: