Interesting.
It is curious that trezor suite does not support lightning payments yet. Anyway, you can use your trezor wallet with Electrum or some other wallet which supports lighting to buy stuff in the store.
That's because it doesn't work. If your node isn't online at all times, you can be cheated by the channel partner. 'Online' in this case means you need to have software running as well as access to private keys. With a hardware wallet, it would mean it needs to be plugged in at all times and have the ability to sign transactions without user interactions, which would be a huge security risk / attack vector.
I guess it could be possible to run a watchtower that notifies you in case of a cheating attempt somehow, but it would be less than optimal. Also always keep in mind hardware wallets can give a false sense of security ('now I'm unhackable...') and the risk of lost funds is a bit higher in LN than otherwise, so I feel it's justified that HW wallet manufacturers want to stay on the safe side.
