Prepare the Liver: Rinse the lamb's liver under cold water and pat it dry with kitchen paper. Trim any tough connective tissues.
Season the Liver: In a shallow dish, mix the flour with salt and pepper. Lightly coat the liver slices in the seasoned flour, shaking off any excess.
Cook the Onions: In a large frying pan, heat one tablespoon of oil over medium heat. Add the onions and cook for 10-15 minutes, stirring occasionally, until they are soft and caramelised. Remove the onions from the pan and set them aside.
Cook the Liver: Add the remaining oil and butter to the pan. Once the butter has melted, add the liver slices. Cook for about 1-2 minutes on each side, or until browned but still slightly pink in the middle. Avoid overcrowding the pan; you may need to do this in batches.
Combine and Finish: Return the onions to the pan with the liver. Add the Worcestershire sauce and stir gently to combine. Sprinkle with fresh thyme or parsley if using. Cook for another minute, ensuring the liver is cooked through but not overdone.
Serve: Serve the liver and onions hot, accompanied by creamy mashed potatoes and steamed green beans for a complete meal.