'as a member of the Eb Lydian scale'. Doesn't compute here, F dominant 7 chord is a V7 of Bb Ionian.
In diatonic language F7 forms a perfect cadence with Bb Major. Russell does not dispute this. however when converting scales to chords on a chord by chord basis Russell's theory of 'vertical tonal gravity' his view is that F7 has the Eb(Lydian) as its true tonic and not the Bb Ionian which is considered a modal scale belonging to the Eb Lydian tonic. The same set of tones yes, but a different perspective on what is the tonic.
Bear in mind the Eb tonic here is not conceived as a diatonic 'resolution' but a chromatic tonic, a centre of gravity towards which all possible intervals of the chromatic scale are judged to be in either a close or distant relationship.
In the second part of the book he talks of 'Horizontal Tonal Gravity'. This is where the parent Lydian Chromatic Scale is determined by the resolving tendency of a sequence of chords . In this situation (somewhat confusingly for me!) the parent Lydian Chromatic scale covering the whole Cm7 F7 Bbmaj sequence
would be Bb.!! However the 'inside' scale choices would not be b5 Lydian based. They would be either Bb Major, the Bb Blues Scale, or any other scale which contained a perfect 4th (presumably to emphasise in the Eb). Beyond that the note choices would be determined by the wider palette of intervals in the Bb chromatic scale.
There has over the years been considerable debate for and against the idea that the Lydian scale is most consonant with the Major triad not the Ionian; and a lot of science put forward to justify each position. I judge it on what my ears are telling me and it seems that Russell has discovered a tonal order within the chromatic scale from this starting point. Besides it really isn't that different from what was already known; that as you go further round the circle of fifths from the home key in a sharp or flat direction you become tonally more distant from that home key. All that really changes is the Lydian starting point. It's the ability to see all the tonal possibilities of a key centre as a spectrum of 'inside' to outside' note choices where you can consciously control the degree of dissonance that made Russell's theory so invaluable at the time.
Alan