I agree with the other replies. If you are based in Luzern, there is NO reason to go to Interlaken itself for a day. The town itself is not nearly as nice as Luzern, and both are on lakes, so you don't need to go to leave Luzern to take a lake cruise.
If you are going to the Lauterbrunnen Valley, that's great, and you need not go up the Jungfraujoch to make it a great trip. If the Schilthorn is too expensive or time consuming, you can go up the Allmendhubel, which is a cheaper and shorter ride that still gives great views of the three peaks. Even a walk along the valley floor is worthwhile, and there's a bus all along it, so you can walk as far as you like and then take the bus back when you get tired (this would be my top recommendation for this area for anyone with potential stamina issues).
If you are interested in the Ballenberg Open Air Museum (old houses and structures from various parts of Switzerland), that's another worthwhile daytrip from Luzern. You take the train from Luzern to Brienz, then a bus from there right to the gate.
While in Luzern, in addition to Mt. Pilatus, you can also go up Mt. Rigi. From Luzern to either Riti or Pilatus, you will cruise on Lake Luzern, which is very nice too. Just be sure that if you're going to Rigi, you take the boat to and from Vitznau, NOT Weggis. Between the train station and boat dock in Vitznau, it's a short and nearly level walk. Between the train station and the boat dock in Weggis, it's a VERY steep and long walk (took me 10 minutes downhill; would have taken me 20 minutes, at least, uphill).