If Lutzow did engage a US cruiser with the mark 21 in say late 1942 in either North Atlantic or in the Arctic convoy area, on a one to one basis, would you favour Lutzow? or would the balance be tipped?
That's quite a difficult question to answer. The problems with the Mk21 were not solved until the introduction of the sealed Mk21 Mod 1 in mid 1943, so in any action before then, one would be taking one's chances. If your store of shells and fuzes had only recently been delivered, you might not experience a higher than normal dud rate, as the question here is shelf life. If the shells and fuzes had been together in the magazines for five or six months (in the USN shells were fuzed at the muntions depot before being sent out to a ship), corrosion would have set in greatly increasing the tendency of the shell to be a dud. The other problem with this fuze was it did not have a graze action feature like the German C/38 BDZ, which meant that at very oblique impacts, such as the shell which glanced off of Jean Bart's barbette capping plate, the fuze would be unlikely to function at all. On the other hand, not having a graze action feature did make the fuze more robust and less subject to fuze damage at low angle/high velocity impacts than fuzes with graze action. It was something of a trade off depending on which was more important, reliable functioning at low angle impacts or reliable functioning at oblique impacts.
The Mk 21 Mod 1 had all external joints sealed with a coating of Bakelite varnish over lacquer.
Given that any engagement taking place in 1942 would essentially see the US ship possibly entering deadly combat seriously handicapped by defective fuzes (sort of like a prize fighter entering the ring with a broken arm), I would have to favor the Luetzow. At closer ranges, the Mk 21 Mod 0 might perform well enough, as was the case in the Washington vs Kirishima, but at the same time this would subject the US ship to accurate 28cm shell fire and possibly torpedo attack--a lethal combination.