It does depend on the engine, some have oil systems that are designed to acccomodate heeling to a degree.... but some don't. Others, for some reason, like to dump all the oil out into the bilge/engine pan if heeled too far on one tack or the other.. a messy lesson best left unlearned.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)