Lake Fulmor is actually a reservoir that was formed in 1947 when Indian Creek was damned for the construction of Highway 243. It is named after A.C. Fulmor, the county surveyor who surveyed the road route in 1933-34 and suggested that damning Indian Creek at that point would shorten the road and produced an artificial lake.
As long as you have a valid California fishing license, you can fish in Lake Fulmor, which is stocked with various fish species by the California Department of Fish and Wildlife. You will need a Wilderness Adventure Pass to park at Lake Fulmor. The closest location to purchase a pass is at the Pine Cove gas station, 5 miles south of Lake Fulmor. Swimming in the lake is not prohibited but discouraged as there are no lifeguards on duty and the water in the lake is of dubious quality.