Yes, it's about time I covered the Lydian b7 scale. It's the third mode of the melodic minor scale, and since I'm showing it in F#, this means that it comes from the Eb (or D#) melodic minor scale. The lydian b7 scale is a great way to take a static dominant 7th groove a bit outside to create some great lines. You can also use it to approach a major or minor chord a half step below (but more on that later). The notes for the F# lydian b7 scale are:
F# · G# · A# · C · C# · D# · E
Note that this is exactly the same as the F# mixolydian scale with one exception: the C, which is the #4 (or #11) of the scale. This note is why it's called Lydian. The lydian scale (without the b7) is the 4th mode of the mode of the major scale
and it has a natural 7th. In the lydian b7 scale, the 7th is flatted. Hence the name.
If we take it's characteristic chord using the 1st, 3rd, 5th, and 7th scale degrees, we get F# - A# - C# - E. But the scale is lydian, which means the 4th scale degree is even more characteristic. So if we replace the 5th scale degree in the chord with the 4th scale degree, we get:
F#7b5: F# · A# · C · E
What does this mean? This means that an F# lydian b7 scale will sound great over an F#7b5 chord. But, don't take my word for it. Just play the example below.