As Smaug is about to leave Erebor he speaks of black arrows as though they are associated with lake town. But the footage of Bards ancestor from this film's flashback and the first film are set in dale.
By what assumption has Smaug the Stupendous made this connection.
Correct me if I'm wrong but I believe Lake-town was created after Dale in the context of the movie as a place to where all the remnants of Dale's citizens fled. Therefore, as an all-powerful dragon, it wouldn't be difficult to associate black arrows with the little humans that moved away from the mountain and re-settled. They are still the same people, and still the same blood (for Bard at least). Smaug is aware of a lot of things it seems, in the movie, reacting rather powerfully to the term Barrel rider, etc. Therefore, I expect he is cunning and careful in spite of his hubris.
When Bard kills Smaug, he does so with his special black arrow which never failed him before. He also says it was from his grandfather. After all, Dale and Laketown are connected, and Bard is a descendant of Girion of Dale. Here is the relevant text from the Hobbit:
'Arrow!' said the bowman [Bard]. 'Black Arrow! I have saved you to the last. You have never failed me and always I have recovered you. I had you from my father and he from of old. If ever you came from the forges of the true king under the Mountain, go now and speed well!'
Since dragons somehow know a lot of things, he probably knew that Bard was a descendant of Girion.
