Let's imagine your Channel is like your Account/ID in that game. If you close your channel and did not sell every item, the Data is gone forever. The thing I dislike about this approach is that the game seems to be bound to some "master nodes" which kind of defeats the purpose of a decentralized game. It should also be possible to link NFT Items to an account (via BTC signing) even if the channel gets closed, but a tx on the mainchain should be maybe a backup solution if everything fails.

I did not test it by now, but it should be possible to use the "Memo" of an LN tx to store a Hash of what ever I want. I guess this alone should be enough to send NFT Data via LN. What concerns me is the part of opening a Channel. The question is: To whom?

Even a P2P Game that uses its Players as Host would eventually delete Data of other Users, which seems pretty unenjoyable  Maybe some LN users would host these "Account Channels" to gain Traffic (= tx revenue) on their node? I don't know by now.