There's no invite options. If someone has their lobby open there will be a little yellow icon next to their Lounge in the community option of GT Mode when you select their name from the list.
I have a question:
When you join a room how do you choose which car to race with. When I opened the menu there were only the favorites cars. Do I have to choose the car before I join or at least set it to favorite?
From what I've seen theres a list of like 40 cars to pick from (not sure if this refects your cars in arcade or not)... but theres also shuffle mode where it picks your car for you
