Rock, the .338 Lapua case is almost 1/4" longer than the .458 Win Mag. Also, most of the good .338 cal bullets are very long. Check the length of the mag well in your rifle, and the length of the ejection port. My guess is that the action won't take a .338 Lapua in the mag well with any high B/C bullet. If that is the case, you would have to single-load the rifle, and probably couldn't eject an unfired round through the ejection port. You'd have to pull the bolt out the back with the round in it.
Even if it will go in the mag, it may not feed right. It's longer and fatter. Modifying frame rails is tricky.
Almost forgot. The bolt face would have to be opened up for the .588" Lapua base diameter.
Good luck, Tom