It’s not easy to find another adjective, “Centralized” comes to mind but that may sound negative, though it’s as accurate as hosted.
“Mediated” is more ambiguous.
I’ve never heard of “Betwixt” before; between (two people or things).
Discussion
"Custodial" is the most neutral that comes to mind.
It tells you the wallet and the funds are essentially owned by someone else.
Seems to be the main point of adding the extra adjective in the first place. Otherwise you'd just say "wallet" or "LN address", done.
in this case though we need a distinction between services that custody users funds entirely and those that provide a lightning address that resolve to a user's own wallet/node back home
> somewhere in the middle are services that run the web server for people who run their nodes at home behind their routers
LN Address Bridges?