When are you allowed to remain on the left-hand lane in this situation?

You answered correctly. You are only allowed to remain on the left-hand lane if your vehicle, including its load, has a maximum width of 2 meters. The important rule here is that the restriction is based on the actual width of your loaded vehicle, not just what is listed in the registration papers. On German roads, such signs indicate which vehicles may use certain lanes, and it always refers to the total width in use at the time. So, always make sure your entire vehicle with any load does not exceed the limit displayed on the sign to legally stay in that lane.