the protocol is tlv-over-nostr: all you need is string manipulation and crypto primitives. running a node in a browser seems unlikely to be satisfying, because nodes should have better availability that that would provide. there's an interesting angle here though... 🤔 fees are set by a node. if you didn't care about offline receive, you could have a low availability node where you and some liquidity provider are the only people on it ... now there are no fees and you only need to maintain the availability standards of whatever liquidity provider joins your ledger. it creates a spillman-like environment with the ability to send funds to any key. but you'd have to rotate every N weeks or lose the ledger to someone else. i don't know if this is better than keeping funds on a ledger run by someone else with fees less than 500 sats-per-quorum expiration period, but it's certainly a shape. what's more likely for most people is that they pay 1% per year to a random node and get a lightning-like wallet with no availability requirements or channel / liquidity management. now you can write down your twelve words just as you do on the base layer, except per-transaction costs are 0.005% and 2 sats but, permissionless means no one can tell you how to use it

sorry, to answer your other questions, yes, you can send zaps, receive zaps, make lightning invoices, and pay lightning invoices, among other things. it's lightning without channels. custody without discretion