Depends on how you pronounce "grawn"! The majority American pronunciation, I think, would be with a long a sound, as if you were singing "fa-la-la-la" and holding the last note. I think. Never heard an American singing "fa-la-la-la" so I could be very wrong.
My impression is that, in the States, Laura and Lara are pretty well identical. When I say them, Lara rhymes with Zara (that long a sound again) and Laura in phonetic script would have the -au- like c, only reversed. Wish I could do it in this program, but no luck.
So, my guess for Grainne would be grahn-ya, with our good friend the long a rather than the mirror-image c.