Hi Jade, my husband and I just returned yesterday afternoon from almost the same trip you are proposing. You will have a wonderful time!! We were in Lucerne for two nights/one day and on our day we did the Mt. Pilatus trip... bus, cable car, gondola, luge ride, cog railway and boat cruise on Lake Luzern. With the exception of the luge ride, it was all included on our Swiss travel pass. We got back to Luzern mid-afternoon and had a late lunch at an outdoor cafe along the water in the Old Town, walked around the shops, explored the bridges, etc. Not sure where you are staying but our hotel (Chateau Gutsch) had a beautiful view, so we bought some wine and enjoyed the stunning view from our balcony at the end of the day. If you can get a room with a balcony/view I highly recommend it!
The next day we departed for Murren, which is very close to Lauterbrunnen. We took a bus (free with travel pass) to the Luzern train station. Trains leave hourly and are very easy (also free with swiss travel pass). We didn't make a reservation for a specific train because we wanted to keep our schedule a bit flexible.. perhaps in June when it is more crowded you would need a reservation. I recommend downloading the SBB mobile app so you can check the schedule very easily. One other tip: since we were without wi-fi when we left our hotel, I would choose a train time and then do a screen shot of the itinerary so when we were without wifi I could just pull it up and it would remind me of the platforms, where the changes were, etc. The trip from Luzern to Lauterbrunnen takes about 2.5 hours, past some spectacular scenery. It is two hours from Luzern to the Interlaken Ost train station (as opposed to Interlaken West), but I believe the train ends here anyway so it is very clear. Interlaken Ost is a small train station and when you get off the train the next train will be there waiting for you and most people will be transferring to that also. It is very easy (and I was a newbie and was a little worried!) Then it's another 20 minutes to Lauterbrunnen and you are all set. We continued up a bit more, via cable car and another tiny train to the village of Murren, which I do recommend you visit during your trip!
We didn't do Jungfraujoch as my husband has experienced high-altitude issues in other places (Haleakala on Maui). Instead, we did the Schilthorn and it was just spectacular! We were gifted with two clear sunny days, and were very lucky. The lift for the Schilthorn leaves from Murren so we only had a five minute walk to the station. This trip was 50% off with the travel pass (I think it was 82Euro round-trip for the both of us). The views at the top are absolutely amazing but if you do either Schilthorn or Junfraujoch do it early in the day before the clouds roll in. The Schilthorn had a web-cam at the ticket desk so you could check conditions before committing to a ticket.. I imagine the Jungfrau does as well. We enjoyed the view, had a cappuccino in the James Bond-themed revolving restaurant, and by the time we were ready to descend, the clouds were moving in. We had got there around 9:30 am I think. After our descent back to Murren, we took a nice walk/stroll on a paved path down to Gimmelwald which is an adorable little village.. from there we took a cable car (free with pass) down to the valley floor and got a bus (waiting at cable car station) and visited Trummelbach Falls. We were a bit disappointed in this attraction. It costs 11Euro pp, and even after taking the elevator, you are only halfway up and there are a LOT of stairs to the top, and then a long climb down. You see various "viewpoints" of the waterfall crashing through the mountains, and it IS interesting but honestly after seeing several of the viewpoints they all start to look the same (just water crashing through a mountain!) I think becaue it was such a beautiful day outside we felt like we were wasting our precious time, yet other people do like it. Then we had to wait about a half hour for the bus to come which returned us to Lauterbrunnen. (it is a very cute town, you will like it!) We had lunch on the front porch of the Hotel Oberland, walked the town and admired the stunning waterfall there, then took a cable car back up to Murren. On our second day, we got a bit of a late start, then headed off for a boat cruise on Lake Brienz. We headed down to Lauterbrunnen then to Interlaken Ost (retracing our steps from two days prior). We were headed to the Zurich airport area at the end of the day, so we had checked out of our hotel and then stored our luggage in a locker at Interlaken Ost. It is a two minute walk over to the boat dock (well marked). You can check the boat schedule on the SBB app also.. just type in Interlaken Ost - Brienz" and under "filter" you de-click train and bus so all it gives you is the boat option times. Again, may want to take a screen shot of this if you are without wifi. We had a LOVELY cruise on the lake, it is just gorgeous. Our train pass covered the expense, and as we had a first class pass we were given access to the second floor sundeck/restaurant area. We found this well worth the added cost as there was a large international tour group on the second class deck who were a bit disruptive. (When I was planning out trip, the Swiss pass was running a special so it was only a bit more than the second class than the first). We cruised to the end of the lake (town of Brienz) and had thought about training back but it was so spectacular we just stayed on for the round tip. I think it was about 80-90 minutes each way. When we returned, trains were leaving every half hour towards Zurich so it was very easy. (again, I had screen shotted some of the choices on my phone so I knew where to change trains, etc. but that's just because I am a nervous traveler!) We left from Interlaken Ost, had one change in Bern (very easy), and then continued to Zurich airport. We were staying at a hotel there since we had an early flight home the following morning so a free hotel shuttle picked us up at the airport and brought us back in the morning. Very easy! Have a wonderful trip!