"The object of entering a duel was not to murder your opponent. The point of the whole thing was to defend one's honor. In fact, it really didn't matter if you won or lost. What mattered was following the code." — Alexander Hamilton
Since Lazarus was using Divine Reckoning Blade, COOLMATH had to change his strategy since he could not accumulate damage since it would be almost constantly healed up.
That was the cause of his switch to a one-handed sword and shield; without it, he had no win conditions against a strong opponent.
On the other hand, he could not use the skill himself since he would simply be inferior.
The way damage is scaled in Harbinger's Call is different from ability to ability, and some scale more than others.