The English way is not to use the possessive notation, but to say "on the living room sofa". It is referred to as a premodifier, e.g., time management, college education, kitchen table, living room sofa, etc.
I'm in the US, and I still refer to a living room in some houses or large apartments as a salon, particularly if there are multiple rooms. Occasionally, I'll say "parlor" too, depending on to whom I'm speaking. It is a little old fashioned here though.