Well, you are definately at liberty to do whatever sounds best to you. *The bigger picture is that you can make up your own rules to achieve the sound you want.
That being said, if I were to construct something modally in E Lydian, I would basically stay with the notes from the E Lydian scale, or like you said, the same notes as B major. *If I am trying to make a certain mode stand out as the tonal center, then I use the corresponding mode's root as the tonic.
For instance, if I were in E Lydian, the E major chord based on the Lydian scale would be my tonic chord. *So your other chords would correspond to how the triads stack up for that mode. *The problem here is that your IV chord (subdominant) is diminished, so your common I-IV-V progression is gone. *Try making your four chord major, and then play the flat second derived from your Lydian over it. *For example, you are in E Lydian, so use an A major chord, but play that A# against it. *You could just use it as a passing note and construct yourself an eight note scale so to speak with the regular fourth and sharp fourth. *However, you technically aren't using the Lydian if you do that I guess.
You may be able to get an interesting
chord progression that leads back to the root nicely, but then again maybe not. *I think something like the Mixolydian lends itself better as a mode to center tones around for the major sound as opposed to Lydian. *Of course, look at the natural minor. *It is a mode that you can easily use to center your piece around and still have good chord movement.
It's a tough call about what to do sometimes, but it always depends on your situation. *Like, do you already have a chord progression you are playing over? *If you just wanted to make a point of using E Lydian, then I would use that over the E chord as needed. *There are also a million other things I would do to make it interesting, but they only seem to come to me when I am playing.
Tell us how your song works and what you've got so far and I think everyone will have different opinions that will get you going in different directions. *That way, you will have several ways to think about it and approach.
(Just for the record, I think I recall seeing like some
Steve Vai solos where right when the solo starts, it says "X Lydian." *Not X, but whatever Lydian scale he is using, just to make a point that the solo itself is from the Lydian mode.
