I've had a few horror stories with American Airlines and interlining, while it might just be my bad luck at JFK and LHR, I would recommend checking the luggage to LHR and then dropping it at Luxair. If at all possible, just use your carry on when connecting at London.
In 2007, I had a piece of luggage delayed in London for almost two weeks. Most of it was a total write off and in June of this year, I had a piece of luggage delayed for almost 24hours. I arrived in London at 9 AM on an AA flight connecting to a 5 PM flight on British to Cairo. Somehow, even if the luggage had Rush tags attached, it never arrived.
British staff reimbursed me for the damaged luggage, which I believed was AA's fault. They never gave the bags to British, and AA didn't give me even a few extra miles.

BTW, all the tickets were on the same original ticket...

Sorry for the long story, but LHR luggage connection horror stories exist. It's less stressful just to recheck your luggage once you get to London.