Lyon, Annency, and Chamonix OR Lucerne, and day trips to Berner Oberland?

You'll likely have nice weather that time of year no matter which location you choose, although rain is always a possibility. Depending on which you prefer, any location will be nice to visit. It's very easy to get around in Switzerland, no car is needed. There are palm trees in Montreux and it can get very warm, but if you travel to the mountains, you'll need to add layers the higher you go. You can travel almost anywhere you want to go easily by public transport and can change your plans last minute as unless you are signed up for a tour, no reservations are required.

Thank you so much for your comments.

I am comfortable with flexibility except with the French TGV which requires reservations. We need to use the TGV Lyria to avoid hauling luggage through 3-4 changes if we try to travel to Lucerne

I guess I need to relax and assume tickets will still be available in June?

France and Switzerland are different in many ways. If you decide you will remain in France during your trip, you should book your advance reservations as required. If you decide to travel to Lucerne and other parts of Switzerland, you would book your reservation as required to arrive here, and your hotel stay as you want. In Switzerland, unless you are booking a tour, public transport does not require a reservation. Traveling here by train, metro and bus is quite easy. It is worthwhile to purchase a discount pass and that information is available on this website as well as sbb.ch.
If you decide to visit Switzerland from Nice, you can also travel through Italy. You would need to check transport schedules in this direction if this is an option you think you might like.
You mentioned additional luggage. I am not familiar with storage lockers in France or Italy but you will find them at many of the train stations in Switzerland. If your departure airport is Nice, the tourist office there or your hotels concierge or manager might be able to provide you with information on storage options while you travel.

I understand the rail and hotel requirements. And I have explored traveling to Switzerland through the Italian Lake District but it is complicated to figure that route out. And this trip we need more flexibility. I have booked hotels (with easy cancellations) and we will decide when we arrive based on the weather and what train routes are available. We are experienced travelers and we travel with a backpack and one small carry on. I guess we will just figure it out on the fly after we arrive in Nice. I have been to Lucerne but haven't been to Chamonix or Lyon etc. Is it possible to describe the difference between the two areas. My research leads me to think Lyon would offer more to do if the weather is bad and it would give us an Alps experience if we traveled to Chamonix. Alternatively it appears that Lucerne would not offer as much to explore except outdoor trips and scenery. This is really the core of my question. Do I have the wrong impression?

Chamonix is definitely an Alp experience and worth the trip. Annency is very charming with lovely canals and bridges. Lyon is a larger city with excellent dining options. It's likely you'll enjoy your travels no matter what you decide. Bon Voyage!

Dear Lacleman. Thanks for all of your helpful thoughts. A friend of my actually traveled to Montreux from Nice and recommended it to us. Perhaps that will become an option. Thanks again.

You will enjoy either choice. There is no bad decision here. I have been to both places and they are both delightful.