Looking at page 95 of Russell's book in which he analyzes John Coltrane's solo in Giant Steps in the context of his Lydian Concept. I will go over the first 4 bars in terms of the major scale. John McLaughlin mentions a particular mode movement he finds harmonically interesting when playing over I-IV changes and might see if that applies later. Anyhoo.
Measure 1: B Ionian over the Bmaj7 chord. No argument there. Then he says C Lydian over the D7 chord. But the notes are also D Mixlolydian and D is the starting of the solo line. So he is trying to superimpose his theory on what is a more direct concept.
Measure 2: G Ionian over the Gmaj7 chord. Again, no argument there. Then he says Ab Lydian over the Bb7 chord. But the notes are Bb Mixlolydian. The G note in the solo would be the major 7 while the chord is a dominant (flat) 7. Again Russel is trying to superimpose his theory on what is a more direct concept.
Measure 3: E Ionian over the Emaj7 chord. Again, no argument there. But where does that leave the Lydian Concept.
Measure 4: He says C Lydian over the Am7 chord. But A dorian are the same notes and a logical choice since it is a ii chord in that section of the song. Then he says C Lydian diminished over the D7 chord. There is a b2 and a 3 so the first scale that comes to mind is the Super Locrian famous for being the scale to play over E7#9 chords (made accessible to the public by Jimi Hendrix with Purple Haze, Crosstown Traffic, etc., the 7th mode of Melodic Minor sometimes called Ionian #1.
Russell does say he spoke with John Coltrane in Greenwich Village and discussed music theory, but I am guessing it was about generalities, like the fact that chords are derived from scales versus his particular Lydian Concept which is a layer of theory on top of actual music theory. In fact I was messing around with the circle of 5ths and 4ths and easily could have come up with a Mixolydian Concept, since 4ths are really more relevant than 5ths. Check out The Beatles Paperback Writer. It is just a G to C, a I to IV movement, but with a cool melody it sounds like a lot is going on.