Leading into the second fight between the two, we saw how Mir got under the skin of Lesnar and how much Brock seemingly despised the fact that he lost to somebody like Frank Mir. Add to that the propensity of Mir holding submissions a little too long, and the hatred and rematch hype is already there.
I'm sure Lesnar wants the shut Mir's mouth once and for all by winning the trilogy. Fans love to see two big men who don't like each other too much slug it out. With Mir's improved stand-up and dangerous ground game, he would present a different test to Lesnar who has proved that he can't stand any punches or kicks to the body following his surgery.
Lesnar would be the man he's always been—explosive, powerful, athletic and a terror if he gets someone to the ground. But, that been his issue in the past two fights; he hasn't been able to secure a takedown.
Nevertheless, a third fight would be exciting for fans and a good way for Brock to be able to end his career with a win over a meaningful opponent. But a promise is a promise. Unless Brock's wife has a change of heart and lets the big man come out and play, his career is over.