The lydian dominant scale is great scale to learn as it brings out a very characteristic color or sound.
This scale is built as followes:
In the key of C... C D E F# G A Bb or root ,2nd, 3rd, #4th, perfect 5th, 6th and b7
It is primarily used over C7b5 chord C E Gb Bb or root, 3rd, b5th, b7th (D7b5, second chord in Duke Ellington's "Take the "A" Train).
Notice that it has the same notes as the G jazz melodic minor scale:
G, A, Bb, C, D, E, F# or root, 2nd, b3, perfect 4th, perfect 5th, 6th and 7th So you could say that the C lydian dominat scale is a mode of G melodic minor built off it's 4th degree (they are interchangeable or relative).
It also works well over C7aug11... C, E, G, Bb, D, F# or root , 3rd, 5th, b7th ,9th and #11