A very nice bike tour you can do yourselves. Rent equipment in town and bike toward Stechelberg and back, an easy 3-ish miles each way. (Lunch in the garden at Hotel Stechelberg is nice.)
For another tour out of Lauterbrunnen, look for the path out of town behind the train station and ride along the river as far as you want: Zweilutschinen, Wilderswil, or Interlaken. Take the train back (or ride if you have the energy!). The only caution I would give is that there is a set of rough stairs in the woods near the start and you have to dismount to get down to the river. You can also take the train to Zweilutschinen, Interlaken, or Wilderswil and start your ride there. Pizza in Wilderswil at Luna Piccante is excellent, BTW.
You can ride, I think all the way to Grindelwald. Best to check locally on that.
There are also mountain bike trails. One I know of (and know that I am not a cycler but a hiker) is between Grütschalp and Mürren more or less the route of the Mountain View Trail.
Bike rental source here https://lauterbrunnen.swiss/en/discover/shopping-and-rental.html?filter_categories_1673%5B%5D=lauterbrunnen_rental. The Tourism Office In Lauterbrunnen covers Lauterbrunne, Stechelberg and Mürren. They will have info on guided biking tours.