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.
> You can also use e-cash non custodially if you run your own mint
Running your own mint, using it to mint ecash for yourself does not improve privacy. You might as well run LN node instead and use LN with self custody.
Recipient needs to be online for redeeming e-cash if its issues by untrusted mint.
> though I want to have e-cash if I must use a custodian
Why do you need a custodian in the first place? Whole point of creating bitcoin was to create e-cash with no trusted third parties. You can read old discussions on mailing lists, whitepaper and initial website.
> Users of lightning can benefit from the liquidity without using custodians themselves
AFAIK e-cash is used for small amount. Lightning already gets enough liquidity from boltz swaps, centralized exchanges etc. Ark and Mercury could provide more liquidity in the future without involving trusted third parties.
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The whole point of ecash is not having to deal with the complexities of running your own LN node and having a large crowd to hide among. Everyone can't run their own mint or it wouldn't work.
The only time ecash makes sense is *if you were going to use a custodian anyway* then it is a strict improvement.
But in the context of the core advantages Bitcoin was supposed to provide, outlined very clearly in the white paper, transacting without intermediaries, it is almost a non-sequitur to bring up ecash
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