Ultimately, the reason lighting doesn't work offline is because finality is an unnegotiable in bitcoin (and every other decentralized crypto).

Lightning relies on time locks to give one party time to respond to the other stealing. It's not just me handing you a check and we treat that as money, it's that we change the net balance on the check every time.

Let's say theres a channel with .5 btc on each side. If I want to send you .1, I just sign a check that has .4 going to me and .6 going to you.

But what if I then scam you by submitting the first .5/.5 check? The enforcement of off chain btc is the threat of going on chain. Part of the .5/.5 check is that it's invalid for a day after hitting the chain. That's my window to expose your fraud and punish you for trying to steal.

All of lightning security is that you have time to respond to attacks. That'd why you need to be online - to respond in that short time frame. It could be possible to extend the time lock to give better time to respond, and use a mobile app to watch out but the need to be online isn't going anywhere.

That being said, it's becoming less and less of a burden as time passes to be always online. This is really not the main thing holding back lightning, I think the bigger thing will be improvements on liquidity management and overall UI. Something like Muun is the greatest thing for new users because it is so simple and it "just works" most of the time.