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As an equal opportunity downer, I have to challenge Super's use of language here, this is not an asynchronous payment any more than the K1 in a LNURL-Withdraw link or trusted shitcoin swap is.
Since the receiver must come online to sweep the state, it's not asynchronous, it's a promise not unlike any centralized solution.
The internet does not work asynchronously, it works through re-attempts and re-signaling.
Do I need my full node on 24 hours a day?
The answer is simply NO.
You could easily install https://bitcoincore.org/ or Knots on any simple PC and open it only when you need to do a tx.
Also if you have a friend running a core node, you can connect a Sparrow wallet to it directly (even no need for heavy Electrum server) and transact in peace.
I personally do no push people to run their own Bitcoin Core node, only if is really needed.
Another option is to use Zeus or Blixt or Breez, that are "light" LND nodes using Neutrino as blocks provider. Neutrino is very easy to use for onchain with no need of heavy sync of over 700Gb of blocks data.
Also you can run your own LND node on any PC in neutrino mode, without heavy GBs of data and transact in perfectly fine privacy.
I still do not understand why people with Umbrels & others are still running full core nodes instead of just using Neutrino. Bitcoin Core is eating almost all resources for a node. And a LN node with a neutrino is more than enough to run smoothly a LN node.
A full Bitcoin node is necessary only in specific cases.
Running a core node without opening the port 8333 and give more seeds to the whole network is NOT helping the network as many says... But opening that port comes with more hurdle, bandwidth, IP etc
Presumably since the algorithm is open source one can derive the game theoretic optimal strategies for zapping and find all the Nash equilibria