<<" I want to take a train/bus (not a cab) to airport. ">>
Since a cab will cost around 65 CHF I can understand that choice. Only if you had four or more people and arranged for a larger cab ( van) to handle the luggage and the people, the cost per person, though substantially higher than the train trip, could become more tolerable
As Rockoyster points out, you can catch early trains from Zürich main station to the airport that take as little as 10 minutes ( no stops) or a bit longer ( 1 or 2 stops).
There is also a tram, which I recall is the #10, which is cheaper, but takes about 45 minutes. The train is the way to go.
I definitely would not stay in Luzern the night before you fly out.
I routinely stay in Luzern and take the train to the airport for a later flight....say 1100 or 1200. That allows more margin for error.
Even though the Swiss Rail system is amazingly effective and reliable, there can be delays in the morning rush hour trains, and, if you have to change at Zürich main station , as is possible but not always necessary from Luzern, you add a note of extra concern when you are in a hurry. The trains on the main line between Luzern and Zürich are susceptible to minor delays in the morning rush hour. Usually only a few minutes, but when you are on that train , and it stops between stations and you wait and wonder, it is an unpleasant feeling. You'll get there, and will not be more than very few minutes late unless the whole system breaks down, but it is stressful.
The benefit of staying in downtown Zürich the night before you fly out is the wide availability of restaurants, and sightseeing. You have a choice of less expensive hotels, too.
Time needed at the airport?
Two hours ahead of flight time is normally sufficient. If your airline flies a large plane full of people who all want to check in at that time, the lines can feel like they it take forever. Once you are thorough checking in, it can take a minimum of 20 minutes to 30 minutes to get to your gate. For intercontinental flights, you will likely have to take a short train ride ( 5 minutes) from the main terminal to the building with the arrival/departure gates. There can be lines - 5-10 minutes, at passport control.
I routinely allow two hours for a flight at about 1030, and have time for a leisurely cup of coffee in the terminal. But, I have a frequent flyer status which gets me through the lines at check in very quickly.
So, because I an overly cautious and hate a last minute rush, for a 0745 flight, I'd take the earliest train to the airport in the AM, and have the luxury of a bit of extra time. As Rockoyster poiints out, that is the 0502
I've attached a screen grab of the schedule of early trains on May 25th. As I suspected...the slow one is the #10 tram. Don't take it.