You need 2 things:

1. You need an always available web server (usually with a static or at least stable IP address)

2. You need an always on lightning node to receive funds.

Afaik, custodial wallets can receive offline with background running services (battery hog) but I don't know how reliable that is.

Re: web servers, I don't know anything that can provide web servers on a mobile phone.

I had considered what if we can set up the web server ourselves? But no one has explored or explained how to remotely control a custodial mobile wallet.

It is possible to do non-custodial with lightning address and lnurl and bolt card etc if you run your own node and set it all up yourself.

Maybe it's possible with #breez sdk? I've heard their API is powerful but I've not explored it myself.