I think most states require brakes on a tow dolly if the vehicle on the dolly is greater than 3,000 lbs. I don't think tag, registration or titles have anything to do with it.
That Lincoln is likely well over the 3,000 limit. You need to check your hitch rating also as you may exceed that too. The Lincoln is no lightweight.
I also think brake requirements are for trailers, 5th wheels, 4 down and dolly towing are not necessarily the same. So what you do towing with one method may not be legal when towing with another method.
Additionally, the motorhome chassis manufacturer may have supplemental braking requirements that have nothing to do with the laws of any state.