I found this and was wondering if I could use this while working with Cthulhu and the other Old Ones.
No, it’s not really “R’ylehian” because R’yleh doesn’t exist, and has never existed. It’s a fiction created by a fantasist in the early twentieth century. This was someone’s attempt to derive a usable tongue from the garbled words in Lovecraft’s fiction using linguistic techniques of modern English. You can use it to make contact with the Lovecraftian beasties, though, if you want to because there really is no established way to work with them.
You can also evoke elves with the Elven language found in the work of J.R.R Tolkien, and Mr. Worf with the Klingon language found in Star Trek.