Low-Background Steel

This would be exceptionally difficult, as oxygen is a basic requirement for steel making as we have ever known it. Steel is made from iron mixed with carbon and then heated to melt. Then oxygen is added which burns the excess carbon into carbon dioxide and reacts with all of the other reactive contaminants and brings them to the surface where they can be cupped off as slag. The melt is poured and cooled and you have steel. Early steel processes used air, blast into the furnace with high powered pumps. Modern steel is made with purified oxygen from cryogenic processes (and there are even designs floating around for steel mills which use the turboexpander from the oxygen processing to help generate electricity to drive the mill).

Without oxygen, you'd have to start with very, very clean iron ore (containing nothing but iron and whatever you wanted to alloy with the final steel), and add exactly the right amount of carbon (which is also exceptionally difficult, since carbon is light and the heat will want to make it sublime anyway). Odds are such a steel would still contain so much impurity as to require a second melt in a vacuum arc furnace, which also would dramatically drive up the cost.

While there might be a future making steel like this in space, I'm not counting it as very likely in the slightest to happen in this century.

It's much easier to use exceptionally clean oxygen - the mill could use an oxygen generation process (like a hydrogen peroxide chemical process plant being added to the mill), or by ultrafiltration of the process oxygen (which seems more realistic all told).

Also, what's in the lead? I didn't think we wanted CO2 in lead but I'm really not sure what impurities it might have naturally.

Someone going on a binge from that, through discovering how Kodak found out about nukes from film and low background steel isnt a huge stretch either

So the term "fallout" is actually a pretty piece of propaganda. While a lot of it did or does indeed "fall out", there's still a lot of radioactivity in the air and on the surface from those nuclear tests in the form of fine particulate. It's in the fine dust all around you as 100nm and smaller particles, dancing around the air through Brownian motion. It's all over everything all of the time. It's in the water and the ocean. Nanograms here and there and everywhere. Not enough to really cause you health problems anymore, but plenty enough to increase the background radiation of the entire surface of the planet by a tiny amount.

How it gets into the steel is through the actual blasting of oxygen into the steel - hundreds of cubic meters of oxygen are used per ton of steel made, concentrating those tiny particulates into the steel they're going into and dissolving them throughout the melt, which is precisely why using ultrapure oxygen and vacuum processes could be used to make lower background steel today... if there was high enough demand to justify the absurd cost of that kind of handling. Fortunately though, there was plenty of steel made before the 1940s, and the demand is not all that high since it's usually used as a shielding material and not as large structural elements. As long as they don't remelt it, or do so in a high vacuum reformer, the metal can retain its low background nature.

Intermediate-lived gamma-emitting isotopes (cobalt-60, strontium-90, cesium-137, and so on) are the particular problem children of nuclear fallout in steel making. The cesium and strontium are largely removed by the same processes as steel is made in the first place - they're simply reactive enough to bond with the silicon and carbon and aluminum impurities being removed and will happily exclude the majority of themselves as part of the slag. So while they do contribute to the background, they're not the main problem. Cobalt, on the other hand, is right next to iron on the periodic table and its happy to stay stuck to the iron, even through rounds of recrystallization. Once the cobalt is in the steel, it's in there until it decays away to nickel over the next century or so. (This is also why it's much less of a problem now than it was even 20 years ago; the halflife of cobalt-60 is about 5 years, which means much of it from the nuclear testing is already gone - most of what remains is from nuclear reactor releases and neutron activation products.)

The more sensitive your instrument needs to be, the more radioactive contamination wrecks your instrument, which is already why physics experiments have to go to extreme lengths to keep everything clean of dust and debris, and are often located underground or underwater to avoid exposure to cosmic rays and atmospheric muons decaying. But the even higher sensitivity experiments like dark matter searches and measurements of cosmic background radiation have little choice but to reach for low background steels and lead as shielding material.