I'm thinking that this is because lightning payments are much cheaper and faster than sending payments on-chain. So the savings are passed on to the buyer.

Indeed.  

But 5% is actually a price premium below the level that is commonly found with other No-KYC P2P trading platforms (e.g., on Bisq, where 8% or more above spot can be a more typical price).

P2P_bitcoin

247bf84fda

Its pretty common for p2p exchanges with no KYC to trade a little above spot, no?