A train from Lauterbrunnen to Paris will go through either Bern or Basel depending on which run you select. Trains through Bern terminate at Paris Gare-de-Lyon. Picking up the TGV in Basel will get you to Paris-Est. It's a 6.0hr to 6.5hr journey.
I'll leave it somebody else to definitively answer the Swiss pass question. I just don't think you can use it for another country. I'm fairly sure that you will need Swiss Francs (or your pass) to get to Interlaken Ost from the Lauterbrunnen Valley. Or, you may be able to purchase the whole journey on your credit card. I just don't think that your Swiss pass will get you past the Swiss border. I've seen your other posts. You may want to look at point-to-point ticket costs and compare with the cost of the Swiss pass. It doesn't look like you will be in Switzerland all that long. We were there 4 days and we had 1/2 fare passes. We went on the Glacier Express, went to the Jungfraujoch and Shilthorn. Saved about $80 U.S. dollars.