If you don't care what happens to the lock ring, a large pair of Channellocks or Vise Grips can also be used to remove it. An improvised pin spanner will work unless the cup is really rusted in place, the, the Channellocks will also work.

The fixed cup can be removed via Sheldon's tool or by clamping the flats in a bench vise and using the frame as the lever to turn it out. Remember it is reverse (left hand) threaded.