HodlHodl simply added LN as a payment method.
So the offers are all still just offers to BUY BTC (on-chain) or offers to SELL BTC (on-chain). Nothing changed -- seller's BTC goes into multisig escrow, buyer sends LN payment, seller releases BTC escrow. If there's a dispute where seller claims buyer didn't pay the LN invoice, that's a normal LN method to prove whether or not that is true (using the preimage).
Oh that's true, there's a subtlety: I was remembering the fact that you can't prove that you paid, and not someone else, (because others on the route have a preimage), but here that's irrelevant, because arbitration will only require proof that the payment is made, not that a specific person did so.
Hopefully we get more sophisticated in future, though I didn't expect it yet: there is no good reason not to use on/offchain swap markets for this kind of thing (they kinda already exist, but I don't think any are p2p(?)).
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The hurdle to providing on/offchain swap P2P is that there's (currently) no easy way to escrow the LN without doing it custodial.
If you see the "Crypto-to-crypto methods" of this list includes three P2P exchanges, but the two non-custodial, Bisq and HodlHodl, provide LN only as pmt method, and the remaining one is custodial ... they let you deposit and withdraw with LN, and you pay a fee (1%) when withdrawing BTC via LN.
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In reviewing that, ... it looks like Bisq does not support LN even as a payment method. There is a fork of Bisq, "Misq", ... or even Bisq 2.0, in-development that will handle multiple protocols, including LN.
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I don't think any are p2p(?)
Like this?
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