1)In the legend ,I think, AA´s lightbringer breaks 2 times, and then some stuff happens...
2) The nightswatch too " broke" two times. first time, when Mormont gets stabbed by brothers, second time when jon gets stabbed by brothers...
-> so there clearly are some hints that point to nightswatch= lightbringer
Or it´s just Longclaw or Oathbreaker or some other valyrian swordy
I don't think the Night's Watch is Lightbringer, but if it is then it has been tempered three times:
First, when Jon (of the Night's Watch) killed Qhorin Halfhand. Second, when the brothers killed Lord Mormont. Third, when the brothers stabbed Jon.
Which would mean Jon = Nissa Nissa.
Which would mean whoever takes control of the Night's Watch now will be Azor Ahai. So . . . Stannis?
Which would be quite a plot twist.
But I think sometimes a sword is just a sword and that Lightbringer = Dawn.