Be careful before upgrading the lever as moment too much for the socket. I would try heat first.
If you can get the car outside (and cover the lower part of the tyre with say some wood to prevent damage) then I would poor a kettle of boiling water over the nut. It should be enough to loosen the grease. That has worked for me before where longer levers didn't.
Once off clean off the old hardened grease & reapply but be carefully the splines can be razor sharp.
