The origin of the simple but filling stew known as lob scouse is clear in that it was associated with sailors, but whether it was brought from Northern Europe to the North West of England (and in fact elsewhere in the country) or vice versa is far from clear. It has been around for 300 years or more, so there's little chance the question will ever be answered definitively. There are dishes called Lapskaus from Norway, Labskaus from North Germany, and Labskojs from Sweden. Some of these feature herring, some pork and pork sausage, but all use carrot, onion and potato, the essence of Liverpudlian scouse (indeed there is a poor man's variant called blind scouse that uses no meat, but is still recognizably scouse).
Naturally, given this is a folk dish rather than a classic recipe invented by some famous chef, there are many versions, but the heart of the thing is potato, onion and carrot, filling ingredients that were cheap and readily available. In Liverpool most would agree that lamb - the cheapest cuts such as breast and stewing chops - is the traditional meat, but others would refuse to budge from the stewing beef they prefer. In deference to the maritime heritage of the stew there is nothing wrong with using corned beef, but expect a sloppier end product.
The meat should be cut into small pieces - not minced - and browned in lard, or vegetable oil if you must. Cut the onion into chunky bits that will not disappear totally in the long stewing, and add these to the pan, followed by the carrots in thick slices, and about a quarter of the spuds you are going to use (so roughly the same weight as the meat you will use, as potatoes should outweigh the meat by four or five times - this is a dish to fill and fortify), in fairly small dice. Cover with water and then some, season, and simmer for a couple of hours before adding the rest of the spuds in large uneven pieces to cook in the stew for another hour or longer.
The liquid (please on no account refer to it as a jus) is generally not thickened other than by the disintegration of the diced spuds during the long cooking, but historically in the sea-going version ship's biscuit would have been crumbled in to make good use of that starch and the opportunity to make it palatable (and add a bit more protein to the stew by way of the weevils many contained). Modern palates may prefer a bit more flavouring to the liquid, with a stock cube (or much better a teaspoon or so of Bovril), a few good glugs of Worcester sauce , or even a blob or more of HP sauce. Not wine. The sailors who developed the dish, had they ever got hold of wine, would have drunk it not used it in cooking.
Inevitably some chefs cannot resist fancifying what is simple labourers' fare: you may see beans added; sprigs of herbs and bay-leaves; pearl barley; bacon; even tomatoes. All fine in a stew or casserole, but they make it something other than simple scouse. Given that the people of Liverpool have taken the dish so much to their heart that they are called scousers (originally it seems a term denoting sailors in the port of Liverpool) you should respect the integrity of a simple stew and avoid bunging in whatever the cupboard offers.
Serve piping hot, with thick slices of white bread to wipe the plate, and big pickled onions or pickled red cabbage.