That "lock ring" is actually the cone for the RH bearing. The flats are 43mm apart, so if using an adjustable wrench you'll need a big 15" example. A remake of the official Schwinn wrench used to remove them can be seen here. Once the wrench is positioned, a whack on the end with a hammer usually does the job. A good securely-mounted vise is probably the best tool for really stubborn ones.