Can I get a closed rhinoplasty right after a lip lift, or do I still have to wait like you do for an open rhinoplasty?

I need to get a revision rhinoplasty andI recently found out about lip lift surgery. I really want to get a lip lift surgery, i really need to as my lips/mouth bother me to the point I don't take any pics and try not to go out to events too much. But apparently you have to wait in between surgeries unless you do them at the same time with the same surgeon. My original surgeon who did my rhino does not do lip lifts, so I am stuck. If the rhino is closed, can I do it right after the lip lift?