Hi, Patty. First, you have to determine if your lamp is real brass or brass plated steel. If it is brass plated steel, the coating is so thin that you will probably not be able to strip it without damaging the brass plating so painting may be the best option. You can check this with a magnet as a magnet will stick to steel but not to brass.
If it is real brass, Woodworker's Supply (phone 800-645-9292) sells Brass Ager. This is item # 941-092. I have not used it but you are to soak the brass for 10-15 minutes, dry off and buff slightly with 0000 steel wool. The price is $5.95 plus freight for 8 oz.