Can you replace LCD laptop screen with LED screen?

That would likely not be a good idea. Presumably you would be using "contact paper." The problem with that is that it would reduce your visibility. In addition, you might not get all the air bubbles out. If you have to remove this plastic layer, you would likely leave adhesive behind. What might be a better idea would be to use a large enough, clear acetate sheet and fasten it to the case of the monitor and not the screen.

A makeshift solution may be to put a bag over the monitor when not in use. You would still have to clean it, but it would be protected when not in use.