Generally speaking, lean is used to save fuel during cruise at lower boost/RPM.
Even in late war hotrods like the P47, pilots are advised to run auto-rich in combat to help the engine take the higher manifold pressure and RPM values with less chance of overheating and all the other problems mentioned by previous posters.
Also, there are cases when chopping the throttle might lead to fuel starvation, which is why the mixture lever is backwards in the RAF planes to make it compatible with the inter-locking pins: you chop the throttle and it pulls the mixture lever back into rich so you don't have to think about it.
Long story short, lean is for fuel economy when moving along at a leisurely pace, not for use during combat
The luftie birds usually don't have mixture controls, definitely not the 109/110 and if i'm not mistaken, the 88,Stuka and 111 also lack them, so i guess they are all automatic.