Scales to Play Over Gmaj7#11
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A Gmaj7#11 chord contains the notes G – B – C# – F#. Any scale that includes every one of those 4 tones fits over it — from the root G, that means G Lydian and G Persian. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
Gmaj7#11 is also diatonic to one major key: D major (relative minor Bm). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.