You would have a dead deer or elk on your hands and, if you are shooting heavy bullets, probably with very little damaged meat. The Lapua isn't all that fast, it mostly allows you to launch heavy, low drag bullets that are very efficient at long range.
A few years ago, I shot a small doe at 12 yards with a .375 H&H. The 250g lead bullet made a caliber sized entry hole, took off the top of the heart, and made a caliber sized exit hole. It didn't appear to expand and, other than the little bit that got blown out the exit hole, there was no meat loss at all. Granted, I used ammo that I had downloaded to 38-55 velocity, but I don't think the results would have been much different with a full power load.
IME, it is the lighter, faster rounds that tend to damage meat. One advantage of being "over gunned" (relative to deer) is that the larger stuff tends to kill cleanly while keeping meat damage to a minimum.
Well then, as long as my range gives the ok I'm gonna get my dream rifle...