We will arrive early Sunday morning in Geneva(8:00a.m.). We plan to purchase a Swiss travel pass. What is the best way to get into Lausanne where our hotel is located? Can we use the Swiss travel pass for that?
frugal,
Yes, you should be able to use your Swiss Travel Pass. There are trains direct from the airport to Lausanne with a travel time of about 50 minutes, so it's an easy trip.
When you exit the arrival hall at Geneva, make a left and follow the signs for sbb.ch. At the end of the corridor, bear right and follow to the ticket agent area for the train. You should plan on using any train pass or discount fare care you purchase right away. After you have your pass and/or ticket, the signs will direct you to your train to Lausanne. You will not have to change trains. You did not indicate where your hotel is located in Lausanne but if you have suitcases, keep in mind that there are some very steep hills in Lausanne and taxis are expensive.
As the previous reply mentioned, it would help to know which part of the city your hotel is located. The rail station is located on the side of the hill, above the waterfront area of Ouchy but below some of the hotels that are located further up the side of the hill. There is a Funicular / Metro that travels up hill from the waterfront and that will be cheaper than a Taxi. I used a Taxi when I was there last September as I wasn't familiar with the layout, but I won't need to do that again (provided I stay in the same hotel).
As with anywhere in Switzerland, be sure to bring money as it's not cheap!