You received many good suggestions, I'll just add this...
Lithium grease isn't a penetrate. It won't do much good freeing up frozen locks and will simply make the key slide in easier as you have already found out.
Try some sort of penetrate such as PB Blaster or even WD40. Work your second key in and out several times after spraying.
Should you decide to access the back side of the lock to try to move the lever by hand, make sure the second key you have is inserted so it disengages the tumblers in the lock.
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