Well, according to some marine biologists I've read there is sufficient sunlight down to depths of 650 feet depending on water conditions so no lights required.
What's that you say? Not riding an aqua trike? It tends to sink in deep water?
Just kidding. Yes, I've been in those torrential downpours. Best thing to do is find an overpass to sit under or a nearby gas station, it's not worth the risk to ride in those conditions.