Lorkhan is a god who had his heart torn out and was doomed to roam around Nirn, presumably as avatars like Wulfharth, Zurin Arctus, or Pelinal Whitestrake. Now, Arctus and Wulfharth had their hearts, and each became the Underking when they were lost. Both wanted to be reunited with their hearts, and were sworn enemies to those who took it from them. Daggerfall explains Zurin Arctus's animosity towards Tiber Septim, and Oblivion expands on that with his cursing of Sancre Tor.

From the Five Songs of King Wulfharth:

The book implies that Shor (Lorkhan in this passage) himself was attempting to reunite with his heart (and wreak vengeance upon the dwarves), and that Wulfharth was his general alongside Dagoth Ur. The Arcturian Heresy continues:

And this is the point where he becomes the Underking and swears vengeance upon the Tribunal (the Dwemer either succeeded and disappeared or got their just desserts for tampering with Lorkhan's heart and were wholly obliterated). It just so happens that there aren't any other accounts of Red Mountain where Nords, Wulfharth, or Lorkhan himself were there as far as I know.

One of the more confusing things about the Arcturian Heresy is that the Underking is summoned by Almalexia to defeat Akaviri invaders, but after the events at Red Mountain Wulfharth was a sworn enemy of the Tribunal. Was Almalexia forcing him against his will to aid her, or could it have been a completely different Shezarrine-turned-Underking? How about the Underking that helped Hjalti Early-Beard defeat the Elves and rule a united Tamriel? Or even the Underking that wrote the Heresy?: Ysmir is a title given to several figures including the Last Dragonborn, not explicitly Wulfharth himself.

Was the Underking's motivation for aiding Hjalti simply a bid for revenge against the Tribunal, or did that Underking understand the overall mythic significance? Did the Mantella contain Wulfharth's soul, Zurin Arctus's soul, or both? And if it contained exclusively one or the other, would it make any difference to the Underking? They were both Shezarrines, after all.

Finally, is there any reason for the Underking to come back after the events of Daggerfall?