No, they couldn’t be on LN, but they could be locked in the LN contract.

The lottery, coinjoin mixes many utxos of the same size from multiple users in several rounds and then sends them back in the original amount. So no one knows what they will get back and only one of the participants will be the lucky owner of the used ordinal.

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and once the contract is settled? Cannot be at the end given to someone else?

I thought that the transaction amounts not going back, but to the recipient. Anyway, I did not study it much yet.

Well, lottery of some nft does not seem to me like a useful use cases.

I more think about what they could be good for?