I'm not sure if it should be "Parking Lot 3" or whether it should have a tag "ref=3"

So the tag of "Parking Lot" doesn't sound like an actual name, but more a description of what the feature is.  Just like a baseball field wouldn't have the name "Baseball Field" if it didn't have an actual name.  In this case, the name tag is used to describe what it is, rather than provide a real name.  This wouldn't be correct.

In the situation here, I am not sure which is correct, but meh, I'm just going to leave it as is and not worry about.  Just happy it is on the map at all!  :D