The II-V-I in terms of cadences in the Lydian scale actually exists as VI-II-V (that is, Dorian-Mixolydian-Ionian), but the cadence does not occur on the tonic of the scale (for example, C Lydian scale, we have: A-7 / D7 / G maj). The consequence is that the final tonic station is not C maj but G maj, meaning the secondary dominant (D7) resolves on the secondary triad and not on the primary triad. The absence in the Lydian scale of a dominant that resolves on the tonic triad partially inhibits the tonal power of the tonic triad, opening the tonal horizon to other cadential solutions that are no longer obvious and banal, as in the relationship
primary dominant/tonic, but based on a more evolved concept of tonal tension and release.
In this, one identifies the end of the tonal harmonic concept and the beginning of the modal harmonic concept. The only possible approach to the modal harmonic concept consists in framing it through the CHROMATIC LYDIAN ORGANIZATION OF HARMONY. The cycle of fifths is not interrupted.
C LYDIAN SCALE: C,D,E,F#,G,A,B
C Lydian scale
In fact, if we analyze the intervals: C/D C/E C/F# C/G C/A C/B
we observe that indeed the only tonic is C. Therefore, C is the unique gravitational center of the C lydian scale.
Unlike the C ionian scale where the tonal environment oscillates between the two tonics C and F, in the case of the C lydian scale the tonal environment is not delimited because there is only one tonic.
If we analyze the C lydian scale by fifths, we have: C-G-D-A-E-B-F#, meaning the cycle of fifths is not interrupted.
The Lydian scale is therefore not a harmonically and tonally closed scale but an open one because it respects the interval of a fifth, which is the strongest from an acoustic point of view; it is a scale that verticalizes harmony because it is extracted from the chromatic Lydian scale and therefore contains in a latent state the missing notes that exist in the chromatic Lydian scale, namely: C#-G#-D#-A#-F.
The Lydian scale placed at the center of tonal organization produces a tonal environment predisposed to chromatic alterations which are not simple passing notes but are structured into ALTERED SCALES AND ALTERED CHORDS.
D
Besides, if we extend the ionian chord we have: C-E-G-B-D-F-A, we obtain a dissonant, unpleasant sound.
If instead we extend the lydian chord: C-E-G-B-D-F#-A, we obtain a consonant chord.
This might be sufficient to understand that the right path is this latter one.