Some of the chords in that progression are a bit strange. I'm not sure what you mean by C# m7-5, D#m7-5, or D7-5. If I interpret all the dashes as flats, then it makes sense, so I assume that's how it was meant. Dash usually means minor, (You often see Cm7 written as C-7) and a fifth can't be minor, so it's kind of wierd to see them written like that.
Anyway, that progression is a bit strange, though interesting. It has a lot of chords, and not a lot of quartal movement. For this reason, I'd say that you should think about each arpeggio when you solo, because the chords don't hang around on any one key signature for any long period of time that would let you sit on one or two modes. It's basically in A major, but with a lot of passing chords. No real tricks I can point out, there's only one ii V I. You can use the same guide tone ideas that apply normally here, though the movement isn't in fourths most of the time so the whole thirds and sevenths connecting won't help you out that much.
If you like soloing with scales, locrian for the m7b5 chords, mixolydian for the dominant chords, dorian for the minor chords, and ionian for those Amaj6 chords will work. Still, with a progression that has a lot of chords like this, I prefer to emphasize chord tones, and think more about arpeggios than chord scales.
As for lydian chromatic, I've never heard of that scale. I wouldn't worry too much about it. It's probably a lydian scale with some extra chromatic notes thrown in. If you're interested in learning scales that come up in jazz and you already know the modes of the major scale, the ones to start with would be the modes of the minor scales. Learn the altered (super locrian) scale, learn the phrygian dominant scale, the lydian dominant scale, the octatonic scales, etc. Don't worry too much about scales though. Scales are easy on guitar, and don't require as much practice as they do on most other instruments. I'd worry more about learning and becoming comfortable with arpeggios. While sweeping them can be fun, it is really impossible to create improvised melodies with it because the arpeggio must be played with all the notes in order from top to bottom or bottom to top. I'd suggest alternate picking each note, and doing excercises like picking every other note, so you always have each chord tone at your fingertips. I find that this helps far more for most jazz than repetetive scalar or sweep patterns.