Watch the Lydian online guitar lesson by Robbie Calvo from The Modal Alchemist
Typically we'd use the Lydian mode to create melodies over the IV major 7 chord or a progression with a tonal center of the IV chord.
I've created a backing track that is a 2 chord vamp, A major 7 to D major 7. These 2 chords are the I and IV in the key of A major.
In this example we are going to superimpose an A Lydian mode (E major scale) over the A major 7 chord and D Lydian (A major scale) over the D major 7 chord. The result of doing this will be to add tension of the D#, #4 (#11) over the A chord and a release effect of consonance over the D chord. It should be noted that the #4(#11) is the characteristic note of the Lydian mode.
Jazz fusion guitarists use this approach to create that feeling of tension and release in their solo lines. It's a pretty cool effect!
Check out the video and take a listen to how the IV mode over I sounds. Try jamming over the track specifically targeting the D# to pull out the Lydian flavor.