After thinking it out a while, I don't see any fair scenario where The Lord Ruler doesn't win.
First off, we have seen how Mental Speed works. Somewhere around pg. 568 in the hardback Well of Ascension, Sazed uses Zinc while fighting Marsh. Earlier in the fight he uses it as well, and can accurately predict the trajectory of Marsh's lamp. Finally, Sazed is filling that Zincmind earlier in the book, and he says his thoughts feel slowed and bogged down.
Second point, an Allomancer of the Lord Ruler's caliber can push on metals inside other's bodies at will. Unless one of these participants are anemic or have another similar condition, pushing on the bloodstream seems like an effective tool to me.
Final two points, Brassminds actually warm up the user, and Sazed says that a Burned Feruchemical charge releases the power tenfold. (Probably a very general assumption, but gives a ballpark range to work off of, as the only other time we might possibly see the combo in action is when the Lord Ruler moves inhumanly fast while fighting Vin. But that could just be Feruchemy, or tenfold speed.)
So in the end, when the Lord Ruler is fighting an Allomancer or Feruchemist; he uses Steelpushes, Zincminds, Ironminds, Goldminds, and Atium/Electrum to defeat them. While facing down an Awakener; Steelminds, Zincminds, Goldminds, Pewterminds, and Atium seem enough to handle most causes. If he does get entangled in an Awakened object, Burning a Brassmind and Goldmind/Pewtermind together should heat the body up sufficiently to set the object on fire, while staying alive. Finally, while facing down an Elantrian; Steelpushes and Ironpulls on the limbs to prevent Aon drawing, or to crush them against their own impenetrable wall, Zincminds or Atium to determine what they are doing and how to counter it, Soothing to distract them if necessary, etc.
As for Nightblood, I think Rashek might be too arrogant to pick up the sword. Why would he need a sword? I see a much more likely possibility of the Lord Ruler Rioting Vasher's anger and causing Vasher himself to draw the sword, then either Steelpushing it out of the way or using other methods to avoid Vasher until Nightblood does the job.
I suppose Raoden could set up a perpetually active metal-transforming Aon, but that smacks a little too much of forewarning on his part, and the Lord Ruler with the same amount of foresight could probably pull off a victory from afar using metal-launched objects, or by crushing Raoden into the ground if he was close enough.