No, the Spear of Destiny (or Longinus Spear) was not in any Doom game. It was, however, in ID software's sequal to Wolfenstein 3D, Spear of Destiny. Near the end of the game, you are transported to a hellish arena where you have to fight the Angel of Death. (Sound familiar? I thought so.) At the end of the battle, you are given the spear to wield. That is why it's in DoomRL. Because you're, y'know, in Hell. And it's a nod to an old and sometimes forgotten ID classic.
And the reason why we don't have the Soul Cube or Artifact from Doom 3 is because Kornel and many of the posters here consider Doom 3 to also be undoomish.
BTW, I've read the doom bible. The game it describes would have sucked. HARD.