A male's enlarged mandibles are used to grip and lever rivals off a branch. That needs reach and grip, and a long jaw is a poor lever: the further the biting surface sits from the joint, the less of the muscle's force arrives there.
Males compensate. Bite-force measurements in the stag beetle Cyclommatus metallifer found the male's closing muscle roughly four times larger than the female's and his input lever more than three times longer, and the male bit at about seven newtons, some six times the female's force in absolute terms and about three times hers after scaling for body size. Equivalent measurements have not been published for Lucanus cervus, though it is built the same way.
The dimorphism is real, but its cost is metabolic rather than mechanical. Females, with short stout mandibles, bore into decaying wood and can draw blood from a finger, which a male's unwieldy antlers often cannot grip. Nearly the whole life cycle happens out of sight as a larva in rotting hardwood, typically over three to six years, which is why the species declines when dead wood is tidied away.