Well DLR systems have relays yes but they also have fuses and may have one for each side too.Also it could be the relay just find it funny it not kill both lights is faulty but again electronics has it own mind and can be internally faulty is just one area.
Hope that helps and best of luck.By the way if my regular headlights fully worked and I had one DLR not working I'd sure try the fuses first and don't just check them visually use a test probe etc or simply change them with a known good fuse the same amp rating.
