Validate our 5 day and 2 half day trip in October

In your place, I would go for no more than two locations in 5 nights. Hikes and views are unsurpassed in the Lauterbrunnen area. There are several villages to explore: Gimmelwald, Mürren, Grindelwald, Lauterbrunnen, Isenfluh to name a few. We much prefer it to Luzern, but many like Luzern, too. Maybe 3 nights Lauterbrunnen or Mürren and 2 in Luzern.

You would probably get a lot of benefit from a Swiss Half Fare Card as opposed to one of passes.

It sounds like a lovely trip, considering your interests!
You really need an additional one or two more days in Lauterbrunnen to take it in. The views are stunning and gorgeous, but that view is often hidden by opaque dense fog that rolls in over the mountains, often after only a brief time each morning. And it often rains there; that's why the meadows are so bright green. So, as much as I love Luzern, I'd still suggest you change your plan from one full day in Lauterbrunnen to two or three full days there. And you should visit Luzern at least a day and a half. If you can't add any more days to your trip, then I suggest you take a very early train from Lauterbrunnen (there's one at 33 minutes after each hour starting at 5:33 a.m.) to Luzern on Sunday morning, and then on Monday take the 2:10 p.m. train from Luzern, track 4, to arrive at the Zurich airport at 3:13 p.m. (The direct trains run hourly on that route, although you can go at other times if you don't mind changing trains with your luggage on the way to the airport station.)

I agree with the others. Pick two cities and drop the third. Too much time in transit and not enough time enjoying where you are. And Lauterbrunnen definitely deserves more than part of a day. I haven't been to Neufchâtel so I'd probably pick Lauterbrunnen and Luzern.