OK, slightly longer post. At various times, I've done commercial drafting, dug footers, wired rebar, performed wind load and rain run off calculations, done basic carpentry and framing, run household electrical (110, 220) from the service drop to the outlets, plumbing and waste water (complete systems), mortared block, and done roofing (shingle and metal). Oh, and am currently GC on a home build.
Your Avian vet is just like me looking at a house - probably knows enough to do a serviceable, professional job for a LOT of avian species. But its doubtful they have any deep experience in any, unless that species is a personal hobby of theirs. And that avian knowledge is itself a specialization, on top of a lot of general veterinary skill.
My brother, on the other hand does framing to finish carpentry - with enough skill that he's doing cabinetry veneers on customer order personal jets. Compared to him, my skill is paltry. Specialization and experience matters. When your vet sends for labs, its like me calling my brother.
Even here, on BYC where we have a lot of knowledgeable, experienced posters focused specifically on chickens, very few of us get up inside our chickens and poke around much. ...and fewer still have much experience with chicken illnesses that can make much of photo records. I have experienced almost no injury or illness in my flock - when I need advice, I go to BYC's experts on that forum. I'm usually called on regarding nutrition. I just happen to be one of those people that does frequently look inside his birds, and there is a lot of overlap between FLHS and chicken nutrition.
As I said above, its a syndrome. Is the liver soft, often buttery in color and friable (crumbly)? Check. Is there evidence of hemorrhage (internal bleeding)? Check. Is there other evidence of excessive fat in the abdominal cavity? Check. Conclusion: Probably somewhere on the FLHS spectrum.
Causes? There is a genetic predisposition - breeds more likely to go broody, and breeds known for being docile seem slightly more susceptible. I assume "Frankenchickens" (Cornish X) are highly susceptible, but they aren't generally allowed to live long enough for symptoms to develop, and breeder flocks are heavily feed restricted. Gender? Absolutely. Hens are far more likely to develop the condition then Roos. When you think about the mechanics, it makes perfect sense. Hens need to build up internal fat reserves in order to sit a nest for 21 days +/-, Roos don't. Docile birds are less active, and will tend to deposit more fat as result of dietary excess, while their internal organs tend to be less robust.
MOST of the cases we see can be clearly traced to feed as the key factor. Too much fat and carbs for the level of daily activity. Birds over eating low nutrition, high energy feeds in an effort to meet other nutritional needs (like Protein) force their livers to work extra hard to process all those excess calories, leading to formations of fatty deposits and eventual liver failure. and unfortunately, low nutrition, high energy "make at home" feeds is something we see a lot of on the forums. BUT, there are also some diseases which can cause the liver to start accumulating fat, the source of which can sometimes be undesired biologicals they ingested in their feed.
and sometimes, no cause can be identified with any confidence at all.
So don't beat your vet up over it. They did OK.
as to the rest, as I said prior, if you have a flock of hens (more prone) and their activity is limited (don't kick yourself, most owners can't offer their birds as much space as they would like, typically due to zoning and/or limited property ownership), and one has already passed due to what looks like FLHS, given the strong influence of diet in the pathology, restricting high calorie/high fat treats ("scratch", cracked corn, mealworms, sunflower seeds, etc) you are adding to a nutritionally complete feed is a very reasonable step you can take towards the future health of the rest of your flock.
Hope that helps some. and don't kick yourself for not knowing - your Vet didn't, either.