Here's a simple tip to play the Lydian "color" (the #11 note) over a M7 chord.
The idea is to play the minor pentatonic scale a step below the root of the chord. We have a CM7 chord so we play the B minor pentatonic scale.
Use the neck pickup and cut the high freqs with the tone knob if necessary.
I use the Mesa Boogie V-Twin preamp on the clean channel connected directly to the sound card and I'm adding a little bit of reverb in Pro Tools.