Lauterbrunnen/Wengen as base or worth splitting our stay?

I'd stay in Wengen, a car free village in the mountains with more sun, Staying in Wengen only adds 15 minutes to your day trips each way, the time to go from Lauterbrunnen to Wengen.

Having been to all of the above, make your bases Wengen and Luzern. Bern can be a day trip from Wengen if you are bored with the mountains or weather is bad. Seriously, the city cannot compare to what you will find in the greater Lauterbrunnen Valley including Mürren and Wengen. Luzern is very nice and worth a full day if you want to devote 2 nights there. It is too far for day-tripping at almost 3 hours each direction. (Still, it does not compare to the mountains of the Berner Oberland.)

Lausanne and environs is too far for day-tripping, IMO. It is over 3 hours each way from Wengen. Save it for another trip or find more time to spend in Switzerland.

Summary: 6 nights in Wengen OR 4 nights Wengen and 2 Luzern.

I’d check hotel availability before making any decisions. Early May is still considered off season for the Berner Oberland.

Also note that some cable cars and trails will not be open at that time. For example, the cable car from Wengen to Mannlichen opens the end of May. I don’t see the schedule yet for 2024, but it opened May 27th this year.

I agree with Carrie about access to the higher elevation in May. With the Cities you listed, splitting your stays between Bern and Lucerne would reduce your travel time. Interlaken is an option if you only want to stay in one place. For mountain views, consider Murren/Gimmelwald in addition to Wengen

It would be helpful to know what you plan on doing in the Berner Oberland. May is likely too early for hiking (trails closed due to snow), and ski season is over. Many hotels and restaurants are closed as it's between the two "seasons." Stay in Wengen if you can, but don't plan on doing much other than looking at the snow-covered scenery.

Assuming that Lauterbrunnen/Wengen is out because of your timing:
Lucerne makes a great base because it's centrally located, it's compact, and it's such a pretty city. Lots to see, good food and good beer. Zürich is about an hour by train; Bern is an hour and a half; Lauterbrunnen stretching it for a day trip at two and a half hours.

And then Montreaux leaves you central to both Lausanne and Gruyeres.

We were in Wengen May 17-31 this year and it was lovely. While Männlichen was still closed and the BLM between Grütschalp and Mürren was closed for maintenance due to the track work, we kept ourselves very busy with other hikes and enjoyed the flowers (so different from our usual fall trips) very much. We had terrific weather and the waterfalls were magnificent. Plus, there was still ample snow on the peaks.

I would go again in May without hesitation.