LCDs certainly can be damaged, or at least temporarily darkened, by sunlight. We have this problem with stopwatches used for timing in contests, if they are left on a table face up. I suspect it is UV related, but I'm not sure on that. A UV filter would then protect most LCDs designed for operation in sunlight.
As for bike computers, quoting from the Cateye Strada manual:
"Avoid having the computer in direct sunlight for unnecessary or extended periods."