From what I see on Google Street View, that lane is not designated as a bike lane. It appears to be a parking lane from the curb markings and signage and from the positioning of the parked cars and trucks, the lane is not wide enough to accommodate cyclists outside of the door zone. It would depend on the lane condition and traffic, but I would likely ride within that lane close to the traffic lane, but move over well before any parked vehicles. The center lane gives everybody sufficient room to pass.