Luggage lockers or luggage storage in Luzern, Interlacken, Zurich Airport

Generally. if lockers are available, are limited to 24 hour storage. They don't like the idea that you might leave a bomb in the locker as a surprise for other travelers. The other option is an attended luggage drop where your bags can be inspected prior to leaving them. Those attended luggage drop tend to be expensive for multi-day storage. One option that might be available depending on your travel schedule is to leave you extra bags at the hotel you will be using for your departure. If you stayed there earlier and were returning within the week, it is possible they might be willing to store a couple bags for the time you are gone.

But the final question is -- why are you not traveling light during the first three weeks? Traveling light is traveling light. Even when we take cruises, we never have more than three rolling, carry-on size bags. The third bag has the extra stuff we might need for the cruise so it is easy to leave that bag behind if necessary.

Swiss passes can be complicated (and expensive, because Switzerland), be sure to read what Rick and the Man in Seat 61 have to say about them

Lockers are a good option for shorter periods and are available at almost all stations (more size options and credit cards accepted at newer ones, older lockers take coins only). Staffed luggage storage is a better option for longer (12 chf per day) but is only available at selected stations.
You can find prices and information about lockers and staffed luggage storage locations here https://www.sbb.ch/en/station-services/at-the-station/services-at-the-station/lockers.html
There are also lockers (max 72 hrs) and left luggage services at Zurich airport https://www.flughafen-zuerich.ch/en/passengers/practical/services/services-for-travellers/baggageservices
There are also various private storage options but most of those are more suited to storage for weeks rather than days.
Otherwise, as mentioned, a friendly hotel may agree to keep your bags for a few days.

Switzerland recently announced that prices for the Swiss Travel Pass will be about 20% lower next year, as well as they’ll add 6-day options! Check them out in January or later.

I just returned from Zurich and stored my luggage at the airport service center for 5 days. No problems there. Lockers at this airport are for up to 72 hours only.

Thank you, thank you, thank you. All your suggestions are most welcome, especially the Zurich Airport luggage service. If we can leave our two large bags somewhere we can go with just our backpacks and walking sticks.

My husband and I will be coming off a transatlantic cruise followed by a river cruise, Amsterdam to Basel. It's been many years since we've been in Switzerland. We have fond memories of the Berner Oberland and would like to spend a couple days there. And we've never taken any of the scenic train trips. If I have this right they are included in the Swiss Rail pass. We hope to go take the Golden Pass, Luzern to Montreux, make our way to Zermatt, and take the Glacier Express going north towards Zurich. Since it will be early May our Swiss Rail passes should work without reservations? Thank you again for taking the time to write. Any other tips, suggestions or if you think I need a reality check don't hesitate to let me know.

Best regards,
Kathy and Tom

Both Golden Pass and Glacier Express are included with the Swiss Travel Passes. You don't need a reservation for Golden Pass, but they are mandatory for Glacier Express (you can do it online from 90 days in advance).
If you have to drop luggage at Zurich Airport first, definitely think about how that will affect your route. It might be best to construct a circular route starting in Zurich rather than zig-zagging all over, but hard to give advice without knowing how much time you have to work with.
One other thing to have in mind: There are plenty of year-round options and it shouldn't put you off visiting, but just be aware that it is considered 'off season' in the mountains in the first half of May. Higher elevations can still have snow and hiking/walking in the mountains is not always possible. Some cable cars/mountain railways and even hotels/restaurants/shops close after ski season and don't re-open until mid-May or even June, so just double check if you have a specific place you want to visit. It can often be very pleasant in the valleys and still nice walking at lower elevations where there is no snow/mud.
You might want to create a separate post with your tentative plans (what you want to see and # of days) so people can give feedback about trains, routings, etc. Some people might not see your questions about itinerary if they are under this post with the luggage storage headline :)
Happy planning!!

The service center at Zurich airport isn't in the terminal building proper. It's located in the building that houses the train station. The two are linked by a skywalk on the first level (level 1 in Europe) and by a crosswalk on the ground level.