Assemble lead sheet to be tight, but able to be disassembled
In a cross section of a sliding puzzle piece, one will see something akin to tongue and groove on all four sides of the piece. In the image below, there is a partial tongue visible, but your purposes would require full length.



If you create a carrier for the lead panel pieces by bonding plywood (drywall is not wear resistant) to the lead and have the plywood extend on two adjacent sides and have the lead extend on the other two, when fitted together, the edges of the lead sheet will make contact. I suggest that having the lead extend without a carrier of its own is contra-indicated, as lead is also not wear resistant and could be more easily damaged when being moved. You would likely want a four layer sandwich.