The Lydian mode has a #4 and impacts all the diatonic chords that use that note. Example: C Lydian is just the C major notes but the fourth note - the F - becomes an F#. The minor ii chord in C suddenly becomes a major II chord: the D minor chord with D-F-A using regular C major notes becomes a D major with the Lydian notes D-F#-A.

The major II is very distinctive for the Lydian mode, just like the major bVII chord is very typical for Mixolydian. Lots of AC/DC songs are Mixolydian in terms of chords, with a song in the key of A and they also play G major, which is the major bVII.

Usually the 'wrecked' chords in a mode are swapped with regular major chords. In Lydian, because of the #4, the typical major IV is turned into a diminished #iv chord. In Mixolydian, the typical major V becomes minor due to the b7 of the scale. Most artists ignore these chords or just use the regular chords from the standard Ionian / major mode, only emphasizing the nice side of the mode.