Depends on jurisdiction. In my province, our Motor Vehicle Act defines all its regular road rules as rules of the “highway” and it treats publicly accessible parking lots as highways.

“"highway" includes ... every private place or passageway to which the public, for the purpose of the parking or servicing of vehicles, has access or is invited”

Ref: http://www.bclaws.ca/civix/document/id/complete/statreg/9631...