First, get the tomato sauce cooking. Heat two tablespoons of the lard in a wide saucepan and add the onion and chilli.
Let them sweat over a low heat for ten minutes until the onion is translucent. Add the garlic, cook for a few minutes more, and then add the tomatoes. Season the sauce well with salt, pepper, sugar and Worcestershire sauce, breaking up the tomatoes with a wooden spoon to make a roughly textured sauce. Leave the tomatoes to gently cook over a low heat for half an hour, adding a little water if they get too dry.
When you are ready to eat, melt one to two tablespoons of the lard in a frying pan and gently turn the flat breads in the fat. Put them in a low oven, wrapped in foil, to keep warm, along with four plates. Add the tarragon to the sauce and stir.
Melt the rest of the lard in the frying pan and turn the heat right up until the fat is sizzling. Fry the eggs, two at a time, spooning the lard over the top of them so that they turn a golden colour at the edges and absorb some of the flavour. Season the eggs well with salt and pepper.
Put a flat bread on each plate and top with the tomato sauce. Put a fried egg on top and scatter with the grated Lancashire cheese.