Brock Lesnar actually has decent stamina, especially or someone his size. Check out his fight against Heath Herring. Reason why he lost so quickly against Cain is that the dude is a beast. Now Overeem, his stamina is questionable, and it showed heavily during that fight with Werdum. The longer I see this fight happening, the more its in Brock's favor.
btw, the trick to train for the whole fight, not to survive 1 round.