Zaps are implements on Nostr with NIP-57 which just got merged in, only a few wallets are supporting it, i believe WoS and Damus and Snort.

the Lightning Address and LNURL are under a different spec, LUD-6/16, correct me if i am wrong.

All specs can be Found on Github

(I am working on a LNBits implementation, lets see how it goes)