Hi Olly,
Lydian is only different to a normal major key in that it's sub-dominant is sharp. (In C Major the F is F natural, in a Lydian mode the F would be F#).
The reason CMaj - DMaj has the sound your seeking is because the two chords exploit the raised 4th, but also certify the tonic is C.
Eg, playing the CMaj says "this is the tonic, this is the key", then the DMaj says "but it's not C Major, listen to the F#, it's Lydian mode", then returning to the C simply ensures the harmony that the key is certainly C, and we're not just using higher degrees of G Major.
Their are two other chords in C Lydian mode with the F#; F#minflat5, and Bmin. You could use these two chords as well as the DMaj when you want to bring in the Lydian tonality, but the Tonic of C needs to be introduce frequently or the feeling of G Major will start to take over.
One way to remind the harmony that the tonic and key is still C is to play the chords that use the note C, but stick the C in the bass.
Eg, CMaj, F#mflat5/C, and Amin/C.
Hope this helps some.
Shayne.
