I think the effectiveness of the lead-lined robe would depend on what theory of X-ray vision you're using - Is he emitting a beam of something that bounces back (like radar) so he can see what's inside, or is he simply able to pick up the item's natural radiation emissions? Or is it something else?
If he's emitting a radar-like beam, then anything high density or really thick will block it - (DnD rules for magic that can be blocked - three feet of stone, a couple inches of metal, several feet of dirt or wood.) Unless it's something specific to lead itself, like its subatomic makeup, that makes it an especially good blocker.
Then we also have the fictions (I think even in the comics) where lead paint causes Superman problems. The amount of lead in old paint is far less than in lead foil.
There is a similar issue with how much lead is needed to block kryptonite radiation - is kryptonite radioactive in a manner similar to radium or uranium or is it much less radioactive? (if you postulate it's radioactive like radium, then humans are at risk too.) Or does kryptonite obey other, unknown, laws of subatomic physics which allow it to behave as it does? (Not only is it lethally dangerous to Superman, but it's also a long-lived, easy to tap, ostensibly clean, power source and makes a pretty good night-light.)
