Firstly, chickens will hide sickness until they are too weak to do so, so it is unusual for a bird to go from perfectly fine to death's door in a matter of a few hours. They might look fine but usually there will have been subtle signs.
If it genuinely is a very sudden and serious illness one of the commonest causes these days in back yard flocks is Fatty Liver Haemorrhagic Syndrome which is often associated with larger breeds of hens like Sussex and Orpingtons and can be due to a dietary imbalance.... usually involving too many carbs like scratch or bread or whole grain diets, like Scratch and Peck where the hens can pick out their favourite components of the feed and not get a balanced diet. The bird will usually put on thick fatty deposits around the abdomen and vent which can cause egg binding and prolapse. Fat also becomes impregnated in the liver and compromises the structure of it, making it weak and prone to rupture. If that occurs, the hen will usually die within a short space of time and there is nothing you can do to save them.
It is usually reasonably apparent even if you do a necropsy yourself if this has been the cause, as there will be masses of yellow fat covering the abdomen and encasing many of the organs and the liver will have a yellowish green cast and be weak and break apart when you handle it. The abdominal cavity may contain fluid from the rupture. Birds carrying too much abdominal fat will sometimes have soiled but feathers.
If I have a sick chicken that has no obvious injury or obvious symptoms like respiratory distress or discharge, the first thing I do is assess how they are moving or standing and look for anything unusual..... some things will point you in the direction to investigate .... neck snaking usually indicates a crop problem so check crop function to make sure it is empty on a morning before they have access to food. Tail down and vent pulsing usually indicates a reproductive problem. It may be that they are trying to expel a shell less egg which can cause them problems for a couple of days and really take it out of them. They might also be egg bound. A soak in a warm Epsom Salts bath and some investigation and lubrication of the inside of the vent might be beneficial. A wide stance when walking sometimes accompanied by more upright posture usually indicates Ascites, internal laying, EYP or Salpingitis. There will usually be abdominal swelling with these ailments and sadly most will prove fatal sooner or later. It may take months for internal laying, a week or two with Salpingitis or 2-3 days with egg binding.
Check body condition by feeling the breast bone.... if the bird is skinny, there has usually been an underlying problem for some time..... feathers hide a lot If the bird is in good condition, check for abdominal swelling between the legs or around the vent. I do this on a night whilst they are roosting by cupping my hand between their legs and comparing with adjacent birds that are healthy. It will usually be obvious if there is an issue.
Personally. I am of the opinion that unless a hen has been broody for some time, lice or mites will not kill them. Lice particularly are opportunistic and thrive on sick birds because they are not well enough to preen and dust bath to keep them in check. Many people see a sick bird covered in lice and assume that lice are the cause, but in my experience they are a secondary issue and just another indication that the bird is sick.
Assessing their poop is another aid in figuring what may be wrong with a sick bird.
Isolating them can be beneficial to monitor their food intake and poop quality when they first show signs of illness.
I hope it is something simple with your hen like a soft shelled egg and she will manage to pass it and return to normal but if the worst happens or you feel it is necessary to put her out of her misery, I would encourage you to either send her off for a necropsy (state agricultural diagnostic labs are usually the cheapest option for that) or if you are unable to do that, open her up yourself and take photos of everything you find. There are a few threads here on BYC where we share and discuss such photos and often come to a consensus on the actual cause of death or at least identify abnormalities that may be responsible. I can post a link to one such thread if you are interested....
Best wishes
Barbara