I don't see any realistic way he wins this. DC will take him down, easily. He will try to use brute strength, you're right, but even if he gets up he'll be gassed after one or two and won't be able to get back up, I think possibly within one round. I then see DC stopping him with ground and pound or a sub, whichever comes first. I think ground and pound.
DC already fought a guy who was hoping to land an overhand right when he fought Roy Nelson.
The differences between Roy and Lewis are that Lewis is bigger, but Roy times his punches better and throws them faster, and had the ground game to survive three rounds. I honestly think Roy was the tougher fight. A guy hoping to land a big punch who doesn't have Roy's good timing will have a hard time landing it on Cormier. I just don't see him having a longer reach and being physically bigger frame-wise as being enough to let him land what Roy couldn't.
Obviously, I think Cormier could win easily on the feet too, but I expect him to take the surest path to victory and mostly strike just to mix up his takedown attempts.