Well, actually, it's both. A chamber that shoots well with Lapua is not as likely to shoot nearly as well with Eley, and vice versa. The shapes of the bullets are too different, and require different dimensions in the chamber in order to shoot well as a result. While you can take 10 lots of any given ammo and possibly find one that shoots much better than the rest, it is also possible that none of it will shoot very well because the fit in the chamber is poor. Lapua likes a 1.5-degree leade, and Eley likes a 2.0-degree leade, to name just one chamber dimension that favours one round over the other. Eley will not shoot as well with a 1.5-degree leade. Something about the shape of the bullet means the round is upset in some manner by the longer leade. Switching to a 2.0-degree leade for Eley yields better performance. The shape of the Lapua gets along better with the 1.5-degree leade, and shows some performance drop-off when using a 2.0-degree leade, though it does get along better with the "worse" leade angle than the Eley does with the one that is worse with it. You can kind of get away with a 2.0-degree leade with Lapua stuff, but can't really get away with a 1.5-degree leade and Eley. The shapes of the bullets agree/disagree with different things. And they both like differing amounts of engraving. The Lapua likes a relatively small amount, and the Eley shoots better with a lot more.
If it doesn't fit your chamber well you can see wildly different results on the paper. I can take one of my silhouette guns and shoot pretty decent groups with it using Eley at 50 yards, about half an inch. Put Lapua stuff in it and it will happily start dropping lots of rounds 6" or more down from your point of aim. But shoot the same Lapua stuff in the other silhouette gun and it, too, shoots around half an inch. There's nothing wrong with the Lapua that would account for it dropping a lot of rounds really, really low. It simply doesn't fit that chamber in that gun at all. The horrible fit is what's responsible for it throwing so many rounds so far down away from the point of aim. Doesn't matter how many different lots I try of the Lapua in that gun, from SK Standard Plus (what used to be Lapua's low rung in the target line) all the way through Center-X, Midas+, and X-Act. It throws shots super low all the time with any of them. X-Act is the most expensive ammo out there, even more than Eley Tenex from the places I buy ammo. It is insanely good stuff. But it doesn't fit that gun's chamber, and consequently doesn't shoot at all. Get 10 lots of any of them, and they'll all do the same thing. Put 10 lots of any of them in the other gun and it will likely shoot better with one of them than the rest, because it fits ok, and one will fit better than the rest and/or have more consistency in other aspects. But it has to fit the chamber, and the better it fits the better it will shoot. (That doesn't mean the fitting as tight as possible, but rather, fitting the best means fitting so as to produce the best results from it.)