I know the Lapua brass is shorter, but can a short neck work with the 416?

I would have thought the neck would be too short. By my calculations, the neck would only be about .320 vs. the normal .490 (in round figures), down by some 30%. I think the bullet grip would be a bit of a problem under recoil, though pressure at normal Rigby loads is not likely to be an issue in the shorter case. This is pure speculation as I have never tried it myself.

Not sure why you would want to use the Lapua cases as this would not be a low cost option unless someone is giving you the brass.

It's OK now, the brass is gone. I was looking at about half the price of 416 Rigby brass.