Slotted items cease to function
Worn magic items don't necessarily require skin contact. For example, an amulet worn outside clothing still functions. So, some barrier between the item and the wearer is allowed while still allowing the magic to reach the wearer.
Detect Magic is blocked by "1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt".
I think it fair to rule that such a barrier between an item and someone attempting to wear it will block the magic. This is, however, a ruling as the books don't say either way.
Slotless items, it depends on the activation process
If the item requires some sort of manipulation then it won't work while in a lead box. For example, a gem of seeing won't work, because you can't see it. For example, an anatomy doll won't work, because you can;t get at the item to dab a few drops of blood on it.
An item with a command word might still work, depending on how soundproof your lead coating is.
Something that needs to be thrown or placed should still work.
Bags of holding will still work fine, except that you can't actually retrieve or place any items. :-)
Piercing and slashing weapons probably wont work, Bludgeoning ones probably will
A lead-lined sword or axe is useless but a lead-lined mace might be more effective than normal.