While mountain passes are open I guess there are other routes but I think the best route will simply be: highway toward Zurich, highway towards chur, turn off to Lenzerheide.
This is a long drive (for Switzerland). If your only reason for selecting Lenzerheide is the rodelbahn I'd look round for something similar closer by. Can't help you with that as I don't know mountains on that side of Switzerland well but I don't think this type of ride is unique so I'm sure with a bit of a search you'll find something. Check out www.bergfex.com
for a map of and info about mountain resorts as a start if you don't know the names of mountain resorts closer to Lausanne.