Uff!!, it's hard to explain every thing about scales or modes!!, but i gonna take your example...
E Lydian, you can play this scale over a E maj7, but it's not just that, to play correctly any mode, first you have to know what is your musical context, one tip very usefull is to Know what key you are playing,E Lydian= B major, but your tonal centre is E, the scale starts in E, and the main notes of the scale are different from B...its the same collection of sound in another musical context, that's all
Example, Main notes for B Major: B ( I ), F# ( V ) and the sensitive C#, but E Lydian ( same notes ) the main note is A#, this note gives the scale the Lydian Flavor, the specific "color" of the mode, and of course the
chord progression are different also from the progression for B Major
all together, E Lydian= B Major, over major 7 chords ( with 9, #11, 13 )...
i hope you can understand some of the info that i puted here
Bye