To prepare the lamb, start by finely chopping the onion. Sauté it gently in a large pan with warm olive oil over low heat, being careful not to let it color or brown.
Rinse the lamb meat under cold water and pat it dry with a clean kitchen towel. Cut the meat into bite-sized pieces and add it to the pan. Brown it gently over gentle heat, taking extra care that the meat remains pale.
Cover with a lid and cook over low heat for about 45 minutes, adding a little vegetable broth if the pan becomes too dry. By the end of cooking, the meat should remain light in color and the onions should melt into a creamy consistency.
Once the cooking time has elapsed, turn off the heat. In a bowl, whisk the eggs together with the lemon juice, then season with salt and pepper. Pour the mixture over the hot lamb.
Allow the sauce to thicken and coat the meat using the residual heat of the pan. Transfer to plates and serve immediately.