You do not want private owners but with agencies it is always impersonal and you pay more : until 150 % of a month of rent (according to duration)!
I suggest you to search " furnished apartment Lausanne " on Google or in french "appartement meublé Lausanne"
The problem is that you want a short period, in summer and for a "big" family!
Good luck, otherwise there is a camping in Vidy near Ouchy.