I Beat The Lightfall campaign on Legend and have gotten [b]no reward[/b] at all. the triumph says that I have completed all missions on legend difficulty and I got the congratulations screen but have not gotten the exotic or any other reward it says I should have gotten.
Your hunter looks like it hasn't done under siege on legendary - can you go to director->neptune and look on the left side of the map for the replayable missions section. The skull is legendary, click that then click the box above the launch button.
Hover over each mission and check that none of them have 'A Challenge Awaits...' listed as a modifier - if they do then you need to complete those missions before your hunter can claim the 1770 reward. Once all of them are missing the challenge modifier, speak to Nimbus.
[quote] the triumph says that I have completed all missions on legend difficulty[/quote]
Triumph is account wide, you did under siege on legendary on your warlock.