Watch the Maj. Triad: Lydian Sound online guitar lesson by Kenny Wessel from Shades of Jazz
If we take a major triad a step up from a major seventh chord, we will get a Lydian sound. The major triad, when thought of from the root, is root, major third, perfect 5th. But if we play that same triad and now hear it over a Major 7th chord a whole step down from the root of the triad, we get a 9, #11, and 13. For example, we can play an A major triad (A, C, E) over a Gmaj7 chord and we'll get the upper extensions we just mentioned. Try moving back and forth from a G major triad to an A major triad, over a GMaj7 harmony and experiment with hearing the chord tones and the colors.
As triads are 3-note ideas, we can run into a bit of a sticky situation when building lines using these structures. Our lines will end up being asymmetrical (which isn't so bad, actually), as we have an odd grouping of notes that we're using as building blocks for phrases or lines. One way to get around this is to make 4-note phrases out of the triads. You can do this by doubling a note (1351, 3513, etc.) or adding a chromatic leading tone to one of the triad notes (1, b3,3,5, for example).