FLash is better than exhaust, lets you make plays. Lee already have high mobility so most ppl take something else like exhaust or ignite. Ignite is not very strong late game. Lee already has an exhaust from his E. Flash is stronger all around & lets you make plays.

Lee scales badly into late game in general. As such you want to max his early game power instead of getting items that take him strong into the late game. He's all about maxing his early game power. So GP10 items such as Heart of Gold are not ideal on Lee since it will gimp your early game power. Better to skip HoG & get Doran's blade for the extra early game power.

Aegis early cos Lee will be ganking a lot & he has a shield. He already has a slow plus red buff should be yours early. Most ppl are not going to get away from Lee when he ganks. So Phage rush is not necessary unlike other junglers such as Nocturne for example. Since he has a shield, getting Aegis lets his shield be stronger. Plus every time you gank, it gives your team free bonus defensive stats to survive & not die. Nothing is worse than ganking a lane because they need help & you lose 2 for 1.