<<"The reason why I was considering driving from Zurich is because the flights I am looking at would probably land around 10:00 PM.">>
You cannot rent a car late at night.
Depending on where your flight comes from ( Schengen or non-Schengen country) and whether you carry on luggage or check it, as well as where you sit in the plane, you can be at the airport train station in as little as 45 minutes or even less (all things favorable) to 75 minutes or rarely, a bit more if you have to go through passport control and perhaps wait a few minutes for luggage. Luggage is fast at Zürich. Of course, if you are at the back of the plane, they have begun to move your luggage while you wait to get off.
Last connection, with change at Zürich main station is at 2343. If you land at 10, you probably will not make the 2243, could make the 2313, and should have no problem with the 2343.
If you use a Swiss Travel Pass obtained on line, no wait to buy tickets.
If you need to buy a ticket, the ticket machines are fast and take credit cards. Faster than the ticket counters during normal hours. Unfortunately, you can only chooses German,. French, Italian or English. ;-)
Luzern does not have as many lockers as Zurich, but there are a fair number.
They are located out along platform # 1.
The SBB website will tell you how many and what size:
The tab for "Services" gives the opening hours for the left luggage office...not late at night, but good for daytime use if the lockers are full;
The tab for Equipment shows the number and size of lockers:
147 small, 144 medium, and 24 large, as well as prices and dimensions. Make sure you have Swiss coins in your pockets if you use them.
<<"Are the lockers at Lucerne a safe place to store the luggage for may be 8 hours? I have heard that during the peak season they are generally not available. Is it possible to reserve them?">>
September is not peak season.
You cannot reserve them.
Your hotel will surely hold your bags for you if you want to leave them there for a a while.
Maybe stay fairly near the station:
I have used the Hotel des Alpes. Nice rooms, mediocre kitchen. Plenty of other places to eat.
Rathaus Braurei (townhall brewery) was very good with wide variety and reasonable prices. Changed hands earlier this year, and I did not have chance to try them when I was there in December.