Put the chicken in a bowl and toss with the lemon juice and 1 teaspoon salt. Let stand at room temperature for 30 minutes.
While the chicken is marinating, prepare a bowl with cold water. Bring a medium saucepan of water to a boil and salt generously, making sure there is enough water to cover the eggs by 1 inch. Carefully add the eggs, bring back to a gentle boil and cook for 10 minutes.
Transfer the eggs to the cold water, and shake or tap gently to crack the shells. Remove the eggs from the water and, when cool to the touch, peel. Set aside.
Put the onions in a large skillet over medium heat. Cook, stirring constantly, until the onion pieces soften and the excess water is dried.
Add the oil and caramelize the onions until the mixture turns golden brown in color.
Add berbere, garlic, ginger, tomato paste, black cardamom and black pepper, and cook, stirring, for 10 minutes. The berbere will have a much better flavor if cooked longer.
Add the clarified butter (niter kibe) and continue cooking for s minutes
Add the chicken, turning to coat well with the sauce mixture.
Add the chicken stock/ water and bring to a simmer, cover, reduce the heat to medium low and cook at a gentle simmer until the chicken is very tender, about 40 minutes. Remove the lid, increase the heat to medium and simmer, stirring occasionally, until the liquid is reduced and the sauce is very thick, about 45 minutes.
Remove the pan from the heat and add the eggs, turning to coat them in the sauce. Cover the pan and let rest for 5 minutes.
To serve, place the chicken pieces and eggs on injera or serving plates, and spoon the sauce over.