Lydian Mode is one of the 7 modes derived from the major scale. Its interval formula — 1 2 3 #4 5 6 7 — gives it a distinctive sound that sets it apart from every other mode. The characteristic note is the raised 4th (#4) — the augmented fourth / tritone above root, which is what your ear latches onto and identifies as the Lydian Mode sound.
You hear it in: Joe Satriani (Flying in a Blue Dream), Steve Vai, John Williams (The Simpsons theme), Frank Zappa.
Lydian is a major mode — compare it to Ionian instead. Lydian raises the 4th of major, creating that floating quality that major lacks.
Parent major key: perfect fourth below root (parent major = root - 5 frets). So if you want to play A Lydian Mode, find its parent major scale root and use those major scale box positions — the notes will be correct for A Lydian Mode when you emphasize A as the tonal center.
Select Lydian Mode from the Full Scale dropdown — a Pro feature, in all 12 keys. The pentatonic boxes are free.
Open Pentatonic Box →Like all modes, Lydian Mode can be played in 5 interconnected box positions that cover the entire neck. Each box sits within a 4-5 fret span and uses the same interval pattern regardless of what key you're in — only the starting fret changes.

A Lydian on the full neck: each color is one box, red dots are the root (A).

Box 1 on its own. Open A Lydian in the interactive fretboard (Pro) →
Lydian is a major mode, so its matching 7th arpeggio is the major 7 arpeggio (R · 3 · 5 · 7), built on the same root. Aim for those notes when you solo and your Lydian lines outline the chord underneath. For the three-note chord shapes of the same chord, see guitar triads and inversions, and for every pairing see which arpeggio fits which scale.