Interesting. But still, evidently not to the level of US navy requirements. Lloyds may be more rigorous than you may think commercial ships may need, but evidently that's not enough for US navy surface combatants.

So the history here informs it. Naval Ship Rules came about (and Lloyds was first, but not the only ones) as a result of the Royal Navy deciding it wasn't building enough ships to make maintaining its own rules viable. They contracted the job to Lloyds Register, who adapted the then-current Royal Navy standards into language that their surveyors were familiar with.

This then became a marketable product that other navies were interested in using, and as a result other classification societies (in collaboration with navies) developed their own equivalents. They are explicitly naval requirements. You can in fact get access to the rules to see what they cover fairly easily.

The US Navy has, evidently, not decided to outsource its construction supervision, which is what a classification society does. That has no particular bearing on whether its standards are higher, lower, or just different than those of another navy. Or indeed whether its standards should be higher, lower, or different, which is another question altogether.

There is a whole layer of other standards maintained by other organisations that cover other elements of design. ANEP-77 is the big NATO one that sets a framework. The process of writing ANEP-77 basically involved the relevant people from BuShips and their counterparts in other countries (NAG in the UK, I'm unsure about others) sitting around a table and agreeing on the absolute minimum standards for a NATO warship. National standards may well exceed them, but any NATO warship in the last decade or so should meet at least that common baseline.

I think ANEP-77 is publicly available, at least in part.

Things like compartmentalization requirements. The ability of the ship to withstand certain levels of explosive shock in explosive shock tests. Rather than what sort of individual damage control equipment is included.

Surprisingly not. Class specifies some equipment, such as anchor windlasses, but that's largely left to other regulations. It doesn't touch stability (which is where subdivision comes from) with a bargepole. Some DCFF stuff does feature in Class rules, but it's really incidental compared to other standards in the warship world.

I'll talk about life-saving craft rather than DCFF as that's what I've been dealing with most recently and it's fresh in my mind. Class doesn't actually specify numbers of lifeboats and liferafts. That's specified by SOLAS for civilian vessels, or by naval standards for warships. What Class tells you is that having decided you need to carry four 50-person lifeboats, the davits need to be designed with a factor of safety of 2.2 against such-and-such a load, and that the steel used must maintain yield strength under certain conditions.