Using 2 headset wrenches (probably a 32mm, but could be 30/31/33/34mm as well) may make it easier- 2 leverage points to apply pressure to. To remove, you want to turn the locknut counterclockwise, like any other nut/bolt.
you won;'t strip threads with even severe amounts of pressure, but if the wrench slips off the locknut you could end up rounding out the flats. Avoid using a pair of channel locks, vise grips, etc.