So it is not really a bearer asset. It is rather a key to access your bitcoin at a custodial mint. If you give this key to another person he must immediately exchange for his own key or reject the payment. Accepting a lightning payment right away is better UX.
Kinda. It is a bearer asset in that if you lose the token you lose the (claim to the) money.
Accepting a LN payment right away requires online access and interactivity. If you have that then you also can settle the e-cash payment immediately.
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