The Lydian Mode is the fourth mode of the major scale. Taken from its root note we can see that it has a #4 (which translates as a #11 on the chord). This provides a strong flavour and can be used as an alternative to the (more bland sounding) major scale for your solo over this tune.
If we check out the piano solo, we can hear he uses the lydian mode in a very clever way over this sequence. By simply repeating the #11 note as the chord changes down a semi-tone, what was a tense sounding #4 note resolves onto the 5th of the next chord. By using this "common tone" improvisation technique he lets the harmony do the work for him!
I often refer to this concept as the "shifting sands" as the harmony moves underneath the repeating melody. It sounds very effective and also really simplifies the amount of mental processing required when you are soloing.