There are a few things to consider when determining the size of lag bolt for an elk mount. The first is the weight of the elk. A heavier elk will require a larger bolt to support its weight. The second is the type of wood that the mount will be attached to. Softer woods will require a smaller diameter bolt, while harder woods will need a larger diameter bolt. Finally, you'll need to consider the length of the lag bolt. Longer bolts will provide more holding power than shorter bolts.
In general, a 1/2 diameter lag bolt should be sufficient for most elk mounts. If you're attaching the mount to a very soft wood, you may want to use a 3/8 diameterbolt instead. And if you're attaching the mount to a very hard wood, you may want to use a 5/8 diameter bolt. As far as length goes, 2-1/2 long bolts should be plenty for most applications. But if you're mounting a very large or heavy elk, you may want to use 3 long bolts instead.