No chance it's reverse threaded, probably simply rusted to the cup.

Tight lockrings often respond better to steady torque than to the hammer and chisel. The ideal tool for the job is a Var 16 lock ring plier, though the flat lockring wrenches work OK. The better lockring wrenches have 2-4 notches and are less prone to falling of sideways than the more common single hook spanner.

If you don't have a lockring tool, you can use the hammer and chisel, but grind the chisel so it fits into a notch and provide a decent purchase into the inside corner, or face, without either cutting the ring or distorting the outer edge. Before beating up the ring any more run some penetrating oil both between it and the BB shell, and between it and the adj. cup.