Which Airport should I fly into Zurich or Zurich train station ... Destination Lucerne

The train station is located in the airport. It's an easy 1+ hour train to Lucerne. Have a great trip!

Thank you for the reply! Is it too soon to book a flight for a trip end of May 2025? Would the fares drop if I wait or more likely go up? Big Thanks!

No one knows about airlines fares. I am myself looking at flights for May 2025. They were just posted a few weeks ago. I suggest you do research on Google Flights and set up price alerts. Good luck!

Booked the flight if the price feels right or if it is no more than $700 roundtrip

I think that what the OP is referring to is that when you use a flight search engine, like eg. Google Flights, that two options come up for Zurich: Zurich Airport and Zurich Main Station. This because the main Zurich station has an IATA code. But this is not the station at the airport.

Zurich has only one airport but many train stations, so use google maps if you're not certain what you are looking for.

As noted, there's no way to predict airfares. If you set up a google flight alert you'll start to see the wild swings in prices, but after a while you'll also recognize what a "typical" price is and then what a "good" price is. You also need to decide which airline alliance you wish to patronize. The common wisdom these days, if you see a great fare book it, you have 24 hours to think about it and cancel if you change your mind.

Why not just put in the airport code for Zurich? ZRH