LNURL is a coordination protocol that runs on the web - it's not built in to the Lightning Network.

That means it requires some additional web infrastructure on top of the lightning node infrastructure to coordinate the requesting of invoices between servers.

It's not ideal, but it works pretty well in practice - it just means there is some extra stuff to run. A non-custodial wallet could probably do it, but there would be some trust involved (whoever is running the web server).