We've been blessed to visit all but Vienna several times. In case you're still making plans, here are my suggestions for yet another alternate schedule. I would suggest going to Salzburg and then Vienna first to allow things to warm up as much as possible in the mountainous Lauterbrunnen area. Its absolutely beautiful, but one year when we visited in September, they had 7 inches of snow the following week. Although it looks like May is typically in the low to mid 60's as highs, it wouldn't hurt to put Lauterbrunnen as late as possible in your schedule.
Day 1 : Fly into Munich. If you'd like to catch up from your flight, you might enjoy Munich for 1 day. We stayed at a lovely inn within walking distance of Nymphenburg Palace (http://www.laimerhof.de). An easy bus ride takes you to the charming old city. Otherwise you can use a "Bayern One Day Ticket" to get you to Salzburg. Cost: 23€ for 1 Adult in 2nd class, add up to 4 more people for 4€ a person.
Days 2 and 3 : (Assuming you go directly to Salzburg on day 1) We love the charm of Salzburg! See the Getreidegasse shopping street, Mozart houses, amazing cathedrals, Hohensalzburg castle, Maria von Trapp's convent and film's cemetary site)... We even stayed one night in the real Von Trapp home now a B and B. Much to see and do in the area.
Days 4 to 6 : Travel and visit to Vienna (This is when you would need to use a different rail pass or individual tickets. Individual tickets while in Austria might make sense and then begin to use a Swiss pass at - or just past - Lichtenstein when you leave Austria. It would take some homework to decide...)
Day 7; Travel to Innsbruck by train. Innsbruck is a couple hours west of Salzburg. This would break up your long train ride to Lauterbrunnen, and Innsbruck is a lovely town. In addition to strolling through the old city, be sure to visit the Hofkirche with its dramatic statuary and the museum with its folk art and fantastic Christmas creche displays.
Day 8 : Travel to Lauterbrunnen Valley via Zurich and Lucerne (This is an absolutely beautiful, and somewhat lengthy train ride through the mountains! We much prefer the Lucerne route through the mountains. The Bern route is much less scenic.) While we've changed trains several times at Lucerne and had lunch there, other than the famous covered bridge, we haven't seen anything that we would recommend taking time to see in Lucerne. (Perhaps we didn't explore far enough...?)
Day 9 and 10: (If you didn't include Innsbruck you could add a day here.) Spend time in the Lauterbrunnen valley. We love the Zuben chalet in Lauterbrunnen, just 2 minutes from the train station and also the lift to the train that goes to Murren. While many enjoy staying in wither Murren or Wengen, we appreciate the convenience of easily reaching both sides of the valley from the town of Lauterbrunnen. In the valley itself be sure to see the Trummelbach Falls, the only internal waterfalls in Europe. Also the lovely folkmuseum to learn more of the life and history of the valley. The tourist office near the chalet can tell you about any folklore evenings and also weather clarity at the higher elevations (very important if you plan to visit either of the top peaks - pricey but outstanding views!) They can also provide you with hiking maps. We are flat-landers, but its easy to take the lifts up to the higher elevations, walk around and then take the lifts back down. The mountains are breathtaking and the valley is lined with waterfalls. The neighboring town of Meiringen, a short train ride away, is a great side trip with its ancient church and excavations and Sherlock Holmes connection. The next stop north has a wonderful alpine antique shop too!
Day 12 : Travel to Zurich by train late afternoon (we usually stay at a hotel near the airport)
Day 13: Fly out of Zurich
I hope some of this is helpful to you! Whatever schedule you choose I'm sure you'll have a marvelous time!!!