Interlaken: Getting around to towns in the area

You can easily just take the train to Lauterbrunnen, walk to waterfall, then take cable car up to Murren, which is possibly all I'd recommend with limited time, but if you are keen and early risers (time of year needed), you could also hike to Gimmewald from Murren.
https://www.swissasap.com/stories/blogs/murren-to-gimmelwald/
The transport in this area so mindbogglingly good, I don't see much advantage to a tour--it's really all about the views.

This is the most simple answer I could ever ask for! Thank you!

aw, thanks!
Here is train website in case you need it: https://www.sbb.ch/en

What you should do is not buy a ticket to Interlaken, but just buy a ticket (outward and return) to Mürren. In Switzerland you can buy tickets between any two places. And such tickets allow unlimited breaks, as long as you stay on the route.

So what you do Is first travel to Mürren via Grütschalp. Then walk through Mürren, and then either walk or take the cable car to Gimmelwald. Then in Gimmelwald cable car down to Stechelberg. From Stechelberg you take the bus back to Lauterbrunnen for the train to Interlaken and wherever it is you are headed afterwards. The ticket covers all this. If you want you can lay in a break at the Trummelbach Falls to visit them,

So which train do I take from Lucerne to Mürren and back to Lucerne? Thank you for the help.

You will find the answer to any "how to get from A to B by public transit" question on www.sbb.ch

From Luzern you take the train to Interlaken Ost. Get off the train and take the ramp down to the corridor running under the tracks. Go up the ramp to Platform 2A to board the train to Lauterbrunnen. Many of the people on your train will be doing the same thing. But some will be going to Grindelwald so heading to Platform B. These are just 2 areas of the same platform. They split the train at Zweilütschinen, with the front half going to Lauterbrunnen and the back half going to Grindelwald. So make sure you are at Platform A. It is clearly marked.

The train ends at Lauterbrunnen. You disembark and follow the signs (and many of the people) to the cablecar station for the ride up to Grutschalp. You will need to show your tickets to access the cablecar platform up the stairs. When the cablecar stops at the end, get off and follow the crowd to the little train waiting there. It will take you the rest of the way to Mürren.

If you feel like walking partway you can get off at the little restaurant at Winteregg and walk to Mürren. Great views over the valley whether you walk or ride the train.

What amount of time should we allow for departure from Lucerne to arrival at Murren? Trying to get an idea how long the day. We will return to Lucerne after the visit.

you can use the link given you 4 posts above from 2 days ago - posten by WengenK. ask the SBB Luzern to Mürren and you get the exact answer.

just under 3 hours each way. More if you walk slowly and miss a connection.