"Lockring" usually refers to the part that holds a cassette onto the freehub body.
UG freehubs
AFAIK don't have lockrings. They use the smallest sprocket to thread onto the FH body and hold the rest of the stack in Place.
If yours is crunchy, removing the cassette won't do squat. That's not where the action is.
So don't go looking for cassette whips to borrow.
The splined center cavity of yours look like on a freewheel. But freewheels generally do have a lockring holding the sprockets in Place.
So I assume the part you want to remove is the ring with the lettering on.
The correct tool would be a pin wrench. Something like this.
117.B | Facom 100mm Pin Wrench 245 mm Chrome | Facom
If you have some metal stock, it's not that hard to make a crude one.
Success is largely dependent on how stuck things are.
Don't get your hope up.
Some have managed removal with a drift punch.
It's cheap enough to try.
Can't advise on thread direction.
Freewheels generally aren't very well sealed on the inside.
If it was me, I'd put the Wheel flat, then shoot WD-40 at/through the gap between stationary and moving parts until it begins to run off Clean.
Then add some runny oil and call it a day.