We are flying to Zurich, and will immediately head to the valley spending 2 nights there then back to Zurich for another night before flying the next morning
If you are flying in, that is Zürich airport, the station is called Zürich Flughafen. If you are spending a night in Zürich, that is Zürich HB, two different places. Going via Zürich HB to drop off your bags is an unnecessary time-consuming detour. I would drop of your Africa bags at Zürich airport, and then pick them up just before you check-in. I have never used one, but I am sure there MUST be some sort of luggage storage at Zürich airport.
Then travel as light as possible to and from Lauterbrunnen and save the effort of lugging those heavy bags on and off the trains.
One way, go Zürich airport - Luzern - Interlaken - Lauterbrunnen (or Lauterbrunnen - Interlaken - Luzern - Zürich HB).
The route via Luzern takes longer, but is more scenic, via the Brünig pass line. It goes over the pass and beside lakes, the route via Bern goes round the mountains, but is quicker.