Zurich airport to Luzerne

no need to purchase ahead...especially for such a simple and quick trip.

We will do the same trip in May and will buy tickets when we arrive. If there is any difference in price (which I doubt) it's negligible and we would be able to go by the first available train instead of waiting for our train or God forbid miss it.

Juckles, Swiss railways have fixed price tickets, no discount for advance purchase, the price is the same whenever you travel and tickets are valid on any train on the date on the ticket (no reservations needed or in most cases possible).
Just buy a ticket at the airport station (Zürich Flughafen) and get on the next train.

Lookup times here: http://www.sbb.ch/en/home.html
There are two connections per hour from Zürich Flughafen to Luzern, it takes ~70 mins., and costs CHF 30 (full fare, 2nd class).

BTW, the spelling is Luzern. That is the local (German-language) spelling. English language guidebooks often use the French spelling: Lucerne.

Thank you Chris, now I know it all. I did not know the price and must admit I expected it to be lower, but well, I knew Switzerland is not cheap.

CHF 30 is full fare. Depending on how much travelling you are doing in Switzerland, it may pay off to get a Swiss Pass, or a half fare card (CHF 120 for one month which brings the price down to CHF 15, so you have already covered 12.5% of the cost of the ½ fare card).

Swiss railways publish pocket timetables for all of the main stations, listing times to all other main stations. These are given away free at stations.
The one for Zürich Flughafen is available online here: http://www.sbb.ch/content/dam/sbb/de/pdf/fahrplan/gedruckte-fahrplaene/fahrplaene_2017/taschenfahrplaene/ZFH_TFPLFV_3016.pdf.spooler.download.pdf
ON Page 40 you can see the times to Luzern.

Just got to Luzern this late afternoon/early evening after a non-stop flight out of Firsco. As others suggest, no need to buy train ticket in advance. Second class is 30 CHF per person. Our flight arrived essentially on-time (a few minutes before scheduled 3:40 pm) and we were on the direct InterRegio train to Luzern departing the airport at 4:47 pm arriving Luzern at 5:49 pm.

Airport ATM cash machine spit out two 100 CHF notes in responding to my request for 200 CHF. Be forewarned.

We got to the train platform with 10 minutes to spare even starting from the back of a 777. Passport control was crowded and both my bags (including the oversized) were at the luggage pickup by the time we cleared immigration.

We bought tickets from the staffed ticket office using our US chip + sign card. Not the fastest line in that people who know what they are doing use the automated ticket machine.

The IR train to Luzern didn't have much luggage space. The over seat coat racks could fit coats but were not deep enough airline style carry-on bags. I stored my ski box and duffel bag in the space near the train door for bicycles. Others use seat space for bags. Not sure what happens with luggage on a fully loaded train. Note that the SBB timetable website shows the likelihood of a given train having low, high or very high occupancy.

Pre-arrival announcements describe the 1st/2nd class configurations of the train and suggest boarding areas (A, B and C) as does the sign board.

Airport ATM cash machine spit out two 100 CHF notes in responding to my request for 200 CHF. Be forewarned.

Edgar, what is wrong with CHF 100 notes? Some machines give CHF 200 notes. You can change them anywhere. I would rather pay with one note, than a wad of smaller ones.
CHF 50 is the absolute smallest note you will ever get from a cash machine in Switzerland.

Yes, definitely nothing wrong with 100chf notes. Pay for an item with a 500chf and nobody will bat an eye - it's just common. Definitely not like the USA where even $20 bills might not be accepted.

Also, Switzerland is the only place where I've seen ATM's labeled with the kinds of bills they dispense, on the outside (in other words, you don't even have to put in your card).