because F# is the fourth of Lydian and not the fifth, and because i can add a G right next to the F# and i'll be damned if that G is an Abb
i suppose you have a choice: Cmaj(b5), and i promise you there is nothing illegal about calling it that. it happens normally in the real world. (and you can still use F# on the staff in the melody if it goes there). Or, if you insist on preserving the "#4" aspect in the chord symbol, you can say Cmaj(add#4,no5). Although i guarantee if you use the second choice on a chart and give it to a player, you are much much more likely to get a pause and confused looks on the first runthrough. where as if you use Cmaj(b5) it increases the chances significantly that they will actually play what you wanted, the first time through. Sure, it's nice to adhere to proper scale numbering / good enharmonics when you can, but sooner or later you run into edge cases where you have to submit to F#=Gb. There are many more extreme cases, but this is an important one that seems to hit home for you