What is surprising is that to-date, there's still no solution for non-custodial P2P trading using Lightning network ⚡.
Paxful supports LN but they require KYC, and also customer accounts are held in a custodial wallet. Additionally, Paxful charges a fee (1%) when withdrawing on Lightning network (which is on-top of trading fees).
A P2P bitcoin trading platform is pretty much just four things:
Where there is a mismatch between existing non-custodial P2P bitcoin trading platforms and a LN-enabled one has to do with the Escrow method. The on-chain non-custodial P2P platforms (e.g., Bisq, HodlHodl, LocalCoinSwap, LocalCryptos, etc.) employ multisig contracts as the method for providing "escrow", where the P2P platform has one of the three keys (with the buyer having one, and the seller having one). In a normal scenario, seller releases the escrow so the transaction has two signatures, satisfying the 2-of-3 multisig contract. If there is a dispute, then the P2P platform's key is the second key used to either release the escrow to the buyer, or to return the escrow to the seller.
I'll have to re-watch this video, but I couldn't really tell if what Synonym is providing is something that can be used as a tool for building, or if their app(s) are using the framework (OmnitBolt) that is the same framework someone building this LN-enabled P2P platform I describe would also need to use when building.
If you use escrow there is no need for trust history or a rating system for buyers and sellers. The basic assumption of escrow is that you don't trust your counterparty and he or she doesn't trust you, but you both trust the escrow agent.
Having a trust history is still valuable as it is a method of punishing participants that burden the escrow agent.