Not really. There is no technical reason why ecash mints can only accept lightning. They can accept on-chain Bitcoin or even other crypto. It's just an IOU vending machine. Deposit, confirm deposit, spit out tokens.

Of course, but I mean they will give buyers their own ecash wallets and the market will run a mint.

It's just conjecture, but I don't see them just using standard lightning. Then every wallet operator is on the hook for laundering or facilitating illicit activity.