Mineral sunscreen on eyelids is the way to go.
Yes, but only with mineral (zinc oxide or titanium dioxide) sunscreen. Chemical sunscreens will sting like hell if they migrate into your eyes, and they will.
Mineral sunscreens sit on top of the skin and don’t absorb, so they’re much less likely to irritate. Apply a tiny dot, pat it gently near the lash line, and avoid rubbing. A little goes a long way — you don’t need to coat your eyelids like your arms.
Sunglasses with UV protection cover a lot of that area anyway, but if you’re at the beach or skiing, a dab of mineral sunscreen on the upper lid and under-eye is smart. Just don’t go full chemical SPF 50 all over your eye socket unless you like crying for an hour.
Your eyelids get a lot of sun exposure — don’t skip them, just use the right stuff.
