I highly recommend Martha's place! It is centrally located (10 minutes away by foot from the Lausanne old town). It has all the necessary amenities for cooking and dining - including coffee capsules for the Nespresso, which in my experience are not usually provided by Airbnb hosts. The apartment is airy, stylish and very clean, we thoroughly enjoyed spending time there. As others have mentioned, there is a parking garage a couple of minutes away from the flat - we payed around CHF35 for 2 days of parking.
We'd be happy to return one day :)