When it comes to chord scale relationships, LCC is sort of a derivative approach,meaning you think in terms of parent scales instead of modes. Except the basic parent scale is not the Major scale but instead the Lydian. So , what you get is a series of different relationships between any given chord quality and the root on which the parent scale is built. Say, for D minor 7 (Dorian) instead of C major, the parent scale would be F Lydian. What’s interesting-and very far reaching-is the fact that, starting with Lydian he builds several other scales-including Lydian Augmented, Lydian Diminished, W.T., both WH and HW diminished etc-each producing different groups of chords. Now, and this is the good part, when you convert a given chord to a parent scale-like the D minor/F Lydian example-then the entire group of scales built upon that particular Lydian Tonic-F in the example-is available for use as different colors of increasing tension over the basic harmony. That means is that over our D minor 7 we could play F Lydian Augmented (no big deal, that’s just D Melodic Minor) or F W.T or F WH and HW diminshed etc.
Also, there are different ways to associate chords to various Lydian Tonics. Say, for a G7, F Lydian would be one choice-giving the one group of scales to use over the chord-but B Lydian is another. The basic scale to use would be B Lydian Augmented (again, no big deal, that’s just a Ab Melodic Minor, namely G altered) but the rest of the scales built on B could also be used.
The association of chords to Lydian Tonics can be done either on a chord to chord basis or it can be based on other factors like the direction the harmony is heading towards any given moment-say, over a ii-v-i we could think in terms of the i-or the key of the music-say, in a blues we could think in terms of what key the piece is in.
Now, the above is just one aspect of LCC, the one dealing with scales. For some the most interesting aspect is what follows, which basically is pure intervalic playing within the Lydian Chromatic universe-but for this I can’t really talk about.