We will be in the Lauterburren for about 9 days. What is the best train pass to buy for hiking in that area
Do you mean the Lauterbrunnen Valley? If so which town/village are you staying in? 9 days is a lot; where do you intend to hike?
I would suggest the Swiss half-fare card. It costs about 110CHF and is good for 30 days. Provides a 50% fare reduction on all trains and buses including the train up to the top of the Jungfrau and the cable car up to the top of the Schiltorn. With the R/T fare to the top of the Jungfau being about 172CHF, the 50% fare savings goes a long way towards paying for the card. You can also use the card to depart Switzerland. I'm not aware of a hiking pass. However, here is a link to a nice website that describes a lot of hike in the Berner Oberland.
http://www.myswissalps.com/berneseoberland/berneseoberland-hiking.asp?lang=EN