Can you pick up the TGV in Lausanne Switzerland, and stay on the same train all the way to Paris? I know it doesn't travel fast on a lot of the track. Also, does it originate in Lausanne?

Yes. There are two TGV trains, taking less than 4 hours without changing trains to Paris Nord. I believe it does originate in Lausanne.

Check the time table on www.rail.ch

I think you will find that the TGV from Lausanne to Paris arrives at Gare de Lyon. It is a very nice train and makes the trip as stated above, except it does not go to Gare du Nord. The section of track in Switzerland is such that the full speed of the train cannot be realized, but once the train leaves Frasne, it speeds along at TGV speeds of close to 180 mph. The land is flat and the speed is not apparent until you meet another train. Then there is a whoosh sound and I can feel a definite change in air pressure.

Bob is correct: all TGV direct (no change) services from Lausanne arrive at Gare de Lyon.