I have used Extra Self-Stockage
(they are in Ecublens and Préveranges. The owner is Swiss German and has lived in the USA (where he brought back the concept). The main office is at the Ecublens/Saint-Sulpice location.
Easy stock is out that way as well.
If you use Zebra in Lausanne they will be much more expensive that these options on the outside of Lausanne (or at least they were at the time).