Watch the Half Step Down: Lydian Sound online guitar lesson by Kenny Wessel from Shades of Jazz
Another way to deal with playing over these Lydian chords is to play the blues. Since we're using minor pentatonic (blues) scales, why not use our blues licks, bends, slides, inflections, etc. to get into the guitar's wheelhouse a bit? Again, we're playing over the same 16-bar progression: G maj7#11, Bb maj7#11, C maj7#11, to Eb maj7#11. Use your bag of tricks, when you play!