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Remember that lawyers love to put their own stamp on language, and hold on to fanciful usages while pretending they are the clearest, most common parlance.

https://dictionary.thelaw.com/demise/ is quite useful here, but assumes a crucial element: in the British monarchy, the Crown is the original owner of everything. The "conveyance" of a lease is the figurative "sending away" (demis) of some of the rights that were themselves inherited or received from the Crown. When the lease ends, the rights come back to the current owner.

Does that help? They don't mean "putting away" but rather "sending away" the rights.