If you waited a week, the payment would fail, and whoever zapped you would receive their sats back. Or, to speak more correctly, their zaps were never sent in the first place.
Discussion
I just thought of a new question. As long as you claim the payment within 24 hours, are the funds in your wallet at risk if you go an extended period of time without opening it?
Since they are in lightning, yes, in theory, you should open your wallet once every week or two depending on the settings of your channels. If you use an LSP, and you trust your LSP not to rug you, don't need to worry about it. In practice, the attack where somebody tried to rug you by force closing a channel with the incorrect amount of unheard of. I don't know anybody it's happened to. If they are caught (by the blockchain/your wallet), there is a significant penalty, and it's all automatic, so there's really no incentive to try to cheat the system.