Some other suggestions:

Kidspace in Lausanne have a little garderie which you can use just one morning per week. They are English speaking too. http://www.kidspace.ch/

Baby Gym do activities for this age range - there is one in Lausanne.
http://www.babygym.ch/index.html

Vallee de la Jeunesse have a nice hang out area for mums and tots.
http://www.valleedelajeunesse.ch/ind...arents-enfants

Espace Prevention do some classes for parents and young tots too.
http://www.espace-prevention.ch/lausanne/

This place in Lausanne does craft activities for parents that you can take your kid along too (but have a feeling it is for non-walking tots).
http://atelier3petitspoints.ch/

Maison de Quartier in Lausanne does a playgroup some mornings per week.
http://www.maisondequartiersousgare.ch/