As the server says. Permissions like:
/lp group default permission set test.test true server="main-lobby AND arcade-lobby"

Or Like Proxy and lobby = true

idk if that would be a good addition.
You could use the web-editor to have a easy way, to add the same permission for multiple servers, without typing the command over and over again... Just add the permission, change the server and add it again.

Not possible due to the way contexts work.
https://github.com/lucko/LuckPerms/wiki/Context

Best solution is to create a custom server-type context, and then use /lp group default permission set test.test true server-type=lobby"

https://github.com/lucko/LuckPerms/wiki/Context#defining-your-own-contexts

So if im right. then i could have server=lobby server-type=production and server=lobby server-type=development?

[Im on vacation sorry for the late reaction]