Watch the IV - V - III - IV Lydian online guitar lesson by Robbie Calvo from Modal Expose
I wanted to create a Lydian progression that included the characteristic note in the chords. By adding the #4/#11 (G#) to this arpeggiated line I achieved that. You can hear that the groove loops around from D to D so this is definitely a D Lydian progression.
You will need to use the capo at the 2nd fret in order to finger the voicings I played in this example. Use your pick if you aren't a finger style guitarist. Nothing too tricky here just watch your timing against the drums.
The 2nd guitar part is basically power chords with added 9ths. The proper name for these chords would be D5/2, E5/2, A/C#. I'm playing these chords with an edgy rock sound to add definition and punch to the chord changes. Try creating your own parts before taking on the solo section.