Bolt 12 would make this 1000x better
Discussion
With BOLT12 is itpossible to pay a node that is offline (mobile wallet like OBW, Breez or Phoenix)?
Bolt12 is for reusable invoices so you don't need lnurl (DNS, webserver...), it works at lightning protocol level.
Offline payments like those wallets you mention are not really offline AFAIK. Breez, ACINQ and so on act as middleman.
Yeah the async payments need a LSP but every mobile wallet has one otherwise it's really hard to used. The LSP never has custody so it should be a fine tradeoff for mobile.