Having both lights is an excellent idea, IMO. The dolly lights will tell others where the outer edge of the dolly is, and the tail lights on the towed vehicle just might be required by state law in many states.
I know that here, if the load extends more than two feet behind the tail lights/turn signals, lights or reflectors are required (in the daytime a red flag at least 12 inches square is adequate). Yes, the lenses on the tail lights may qualify as "reflectors", but lights are a good idea, especially after dark!
As always, do your research. Check the laws in your state, and comply with or exceed them.