While it is always possible that you could bump into an uninformed employee; the rule is if one is traveling in a sleeper today, then one is entitled to use any lounge in the system. It does not matter if you are arriving or departing, it only matters that you are about to spend or have already spent part of the day in a sleeper. Make sure that you hold onto your ticket stub in order to use a lounge in a city where you are arriving.

It also doesn't matter if one arrived or is about to depart a given city in a sleeper. In other words, if you were to depart Boston, NY, or Philly on a regional train to DC, whereupon you will board the Capitol Limited in a sleeper, then you are allowed to use the lounge in the above city where you board the regional, as well as the lounge in DC. One needs to show both the regional ticket and the sleeper ticket to gain this benefit though.

And yes, even on board upgrades count, although obviously only for arriving cities. You’ll need to show the receipt that you got from the conductor, as well as the original ticket stub.