Yes, Muun functions to receive and send both over Lightning. What they offer is to receive via LN Invoice like you've mentioned and they have an expiry of 24 hours. The other wallets that I linked you to also generate an LNURLp (LNURL Pay) and Lightning Address in addition to receiving via LN Invoice, either of which can be setup on your profile field 'LNURL / Lightning Address (LUD-06)'.

Since you already have a ZBD LN Address, add that your profile LN URL / Lightning address field. That field will not function on Nostr clients to accept a Lightning Invoice currently.