Cashu isn't an upgrade to or replacement of lightning. Mints are lighting nodes. The scenario calle described literally is not possible with LN alone.

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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.