Not really an appropriate framework, one is an open-network, the other is a closed network.

Bingo, this ties back to the end of my previous comment, their entire premise is that the Ark is a roach motel and all activity will go through them, a centralized entity running a closed network.

Yes, much of Bitcoin's value, and all of Lightning's value, is in it being an open network with no central point of failure or trust needed to enter.

Closed networks are centralized applications, which is why they're leaning now into the "DeFi" nonsense as their latest narrative pivot. The use-case for in-Ark payments is user-to-user within a given application, like a shitcoin exchange that has its own network effect of buyers and sellers.

DeFi is a scam word unto itself because there's no actual decentralization.

Entry into their closed network is inherently gated in the case of LN, because of the swap. I don't believe this is the case with on-chain, you could make a sufficiently sized on-chain payment to enter it (paying a chain fee up front). But if you could afford to make that chain fee up front to enter, you for the same cost have just opened a Lightning channel.