Can we resolve the issue towards non-Jews that we should follow their standards towards them? That is, you don’t need to go to the extent of halakhic obligation, but do at least what a normal non-Jew will do, maybe a little more – return to “lost & found”, pick up from the ground to a chair, don’t take it at all …
For a benchmark, see a current story on YWN front page about someone in Indiana finding an old photo that flew 100 miles from Kentucky tornado, posting on FB and eventually finding the owner. However awesome it is, it is slighyl below the Jewish standard that would require spending another 10 minutes googling the name directly instead of relying on power of FB …
Also, I personally benefited from non-Jews calling to deliver a lost purse (in NorthEast) and just not touching a purse on the window for several day (in the South).