LNURLw works if you're offline, but your internet gateway is online to redeem the payment. You can also use e-cash non custodially if you run your own mint

Custody clearly comes with risks, though I want to have e-cash if I must use a custodian, because standardizing the interaction with custodians allows me to leave the custodian frictionlessly and it happens to come with privacy.

Yesterday I witnessed atomic real time channel rebalancing involving mints. Users of lightning can benefit from the liquidity without using custodians themselves.