Three things to consider with a downwind landing. Airspeed of the plane, groundspeed of the plane, and stall speed of the plane.
Airspeed is what keeps it flying, so less lift downwind is not correct. You have to have an airspeed greater than the stall speed to keep flying, and if you're flying downwind, that means a greater groundspeed. The math above, adding the wind speed to the airspeed of the plane is correct insofar as it increases the ground speed, and therefore you'll touch down a lot faster coming in downwind. Not a bad thing to practice on occasion, as sometimes you'll have no options except a downwind approach. Same as practicing for crosswind landings. Get good and comfortable with upwind or no wind landings first, though.
You never Have to do anything
Well, if you're flying, at some point you HAVE to land.
