Since the parking lot and service road still exist then they can be mapped in OSM. The service road was tagged as access=private, which seemed correct from what you describe. I see that someone else restored the service road. 

Once the parking lot is closed for rebuilding, then it would be appropriate to remove the service road. For example, I just removed a school building in Mount Vernon. When I drove by yesterday, it was being torn down.

I see that you updated the fence, which is appropriate, and thanks for that.  