I see a train route described to the airport vs the city itself. Is this something worth trying---- to get on an international flight back home if the flight is at 8:30am? Or is it best to stay the night in Zurich before the flight?
If the train gets there two hours before the flight and you can check-in online then go for that. I have been to Switzerland 4 times since 2017 and the trains are always on time.
I would stay at the airport itself for a flight that early. Better safe than sorry. There's a Hilton nearby with a shuttle or hotels actually inside the airport.
I suggest to stay at the airport. Check the Radisson blu or Hyatt Circle.
8.30 is indeed too early to comfortably reach the airport 2-3 hours before your flight starting from Luzern. The first train from Luzern gets you to the airport station at 6.21: that's too tight for me. I'd spend the last day in Luzern and sleep at an airport (or near-airport) hotel.