When soloing over Major chords and their derivatives we have two scales to choose from. These are Ionian (our standard major scale) and the Lydian scale.
The Lydian Scale is what we'll call our 'Go To' scale for major chords when improvising in a modal context. This means that in a modal context you'll usually want to play a lydian mode over a maj chord and most of it's derivatives. The only time you want to play a major scale is when the 4th is expressed or written in the chord symbol or voicing. For example a C sus 4 chord could be derived from a major triad but if you tried to play lydian over it the #4 of the lydian mode would clash horribly with the natural 4th of the chord. The same is true for a Major add 4 chord. These are rare cases in modal music though, so lydian will usually suffice for most scenarios. The reason behind this is that the #4 of lydian just sounds better than the natural 4th of the major scale in this modal context.
Here are the chords which will accept Major or Lydian Modes. I'd recommend that you print this chart out and place it where you practice as a reference.
|Maj Triad||Major/Lydian scale (Lydian 1st choice)|
|Add 9||Major/Lydian scale (Lydian 1st choice)|
|Sus 2||Major/Lydian scale (Lydian 1st choice)|
|Sus 4||Major scale|
|Maj add 4||Major scale|
|Maj7||Major/Lydian scale (Lydian 1st choice)|
|Maj9||Major/Lydian scale (Lydian 1st choice)|
|Maj13||Major/Lydian scale (Lydian 1st choice)|
|6/9 chord||Major/Lydian scale (Lydian 1st choice)|
|Maj6||Major/Lydian scale (Lydian 1st choice)|