Question to the experts ... What affects your ability to sail off a lee shore, at what point does it become "dangerous", and at what point does it become "impossible", and why ?
As was said, without knowing the lee shore's geography, relative to wind direction - and boat's distance from hard ground, this is such a general question with no correct answer.
By no means am I an "expert sailor", but having singlehanded her for the past four seasons, I did learn how she handles under most conditions. Her fastest point of sail is a close to beam reach using a moderate amount of sail. Full sail under strong winds makes her heel quickly, but will maintain stablility. The deep, modified fin keel does minimize sideslip, allowing for laterally sailing along the lee shore. I would simply point as high as possible and eventually, crab away to safer waters.
Worse case scenario, if sailing proves to be a losing battle and powering is not an option, I'd drop all sail, deploy the storm anchor with 250 feet of chain, and ride out the storm.