Traveling Interlaken to Murren

The Swiss Travel Pass is only valid to inhabited towns and villages in Switzerland. Thus it is valid all the way to Muerren, no matter which of the 2 ways you get there from Lauterbrunnen, either the gondola/train route or the bus/cable car route. However it only gives a discount on the cable car going up from Muerren.

St Maurice does not show lockers at the station.
https://www.sbb.ch/en/station-services/at-the-station/railway-stations/station.1403.st-maurice.html

PS, there are lockers at Martigny station which is 10 minutes away by frequent trains.

No, not all cable cars and trains are covered. The routes to the highest mountain peaks are discounted 50%. This page has a map showing pass coverage. The dotted lines are the discounted routes.

https://www.mystsnet.com/en/download/area-of-validity-swiss-travel-pass-2022/?wpdmdl=42165&masterkey=616edeec5609d

Thanks for the responses. We were going from Zermatt to Geneva and thought about stopping in St. Maurice. Aside from going to Martigny to stow luggage, are there any other suggestion as what to do with our bags if we decided to get off in St. Maurice?

Another option would be to use the SBB (Swiss Railways) luggage forwarding service, and only travel with a day pack + valuables + whatever you need for that night. Luggage left in Zermatt on Day 1 by 6 PM will be available for collection in Geneva on Day 3 at 9 AM. I have never tried that service myself, but I would expect Swiss, i.e. good, reliability from it.

Should add that the station-to-station luggage service is 12 CHF per item.

Note that the discounts on the mountain summit lifts vary by pass: the STP gives 25% discount, but I believe the Half-Fare Pass gives 50% discount. It is a challenge figuring out what pass is best for your individual trip.