Provence base?

I suspect you may need a car if those are all must-sees. All except the Luberon Villages and the Pont du Gard are served by rail, and you can get to some additional places via bus, but usually more slowly. I haven't been to Nimes, which I understand is nice; I think Arles, Avignon and Aix are worth a full day each, so the question is how many additional days you'll need to see Nimes, the Pont du Gard and the Luberon; I'd guess two at a minimum, for a total of five.

I haven't driven in Europe, much less in Provence, so I'm not the one to suggest convenient bases to you, but you've made it easy for others to help you by listing the places you especially want to go.

To my mind, Lyon deserves a lot more than the few hours you'll have there if you make a stop en route. Perhaps it would still be worthwhile to you to have a bit of time there; I'd be too frustrated to enjoy it.

We based in St-Remy and that worked well for all the places you’ve listed

I am with Christine, St Remy is a good base. it offers a good location, nice restaurants, and a wonderful market.

Saint Rémy de Provence as suggested above (most central), or L'Isle-sur-la-Sorgue, Pernes-les-Fontaines, Uzès (far from Lubéron)... all make for good bases. Aix is a bit far from that area, definitely an outlier: I would consider skipping it, even though it is a beautiful city.
Also, I do not think that stopping in Lyon for the night is worth it. To me, Lyon is not the kind of city that you love at first sight (and I personally do not like it much at all but I am in the minority), so a brief stop there does not do it justice.

You can take a direct train from Marseille to Aix-en-Provence (45-minutes) and when you’re ready to move on rent a car in Aix and drive to Arles and make that your base to explore Provence. Here is what Google maps says about the amount of time it takes to drive to:
Avignon (1h)
Pont du Gard (1h) then to Nimes (45-minutes) and back to Arles (45-minutes).
L’Isle-sur-la-Sorgue (1h 15m) then to Roussillon (30-minutes) to Lacoste (30-minutes) and Ménerbes (15-minutes) to Arles (1h 15m).
Lyon (3h 15m)

I recommend St. Remy de Provence as well. It's very pretty with lots of restaurants, cafes, and nice shops. And is a great base for Les Beaux, Avignon, Luberon Villages, and Pont du Gard. You can also visit the asylum where Van Gogh was a patient. It's located in St. Remy along with the Glanum ruins.

Any lodging recs in St. Remy?