Awesome!
So how does this major/minor thing work? Is it some sort of social system? Is it heritable, or is it just whether or not they are born large?

The development of long waterbuffalo-type horns in the male dung beetle Onthophagus taurus depends on the food supply being sufficient to grow the grub to a size that, when it pupates, its pronotum reaches a certain width that triggers the horn growth. Male pronotums of lesser width result in smaller horns or even none at all. I imagine it is much the same for stag beetle mandibles, although the size range would be limited on the downward side owing to the neccesity of developing at least normal female-sized mandibles.

Curiously, undersized scarab males are said to have great success "sneaking" sex with females awaiting the outcome of tussles between major males. In some horned geotrupids, a major male guards the entrance to a burrow containing "his" female, but a minor male will burrow down below him in effort to intercept the tunnel of the female and mate with her while her dumb brute mate stands guard. Perhaps these sorts of schemes are engaged in by minor male stags, but Phillip would know better than I.

Much work has been done on this group and some of the other horned scarabs - while, as a rule, there are some advatanges to having the large mandibles or horns, there is often a developmental cost.

example of rather dramatic minor/major male differences in L. elaphus;

major males have the mandibles large, curving downward, also see head, whereas minor males have the mandibles almost straight without the dramatic head sculpturing.

L. placidus probably occurs in Virginia - listed from NC (as pseudolucanus}.

Perhaps you would like to have a look at this paper:
Knell, R. K., Pomfret, J. C. & Tomkins, J. L. 2004 The limits of elaboration: curved allometries reveal the constraints on mandible size in stag beetles. Proceedings of the Royal Society of London B 271, 523-528. For a pdf file click here.
This study has been done with museum specimens. A lot of hard work, and to me it is not on the fun side of entomology...

a couple more photos with info can be found here and here. L. placidus is besides darker (black) ventrally - its smaller 22-28 mm (w/o mandibles) Additionally, I'm not sure L. placidus is known from Virginia.

There are a couple of nice major males in the guide;