In a large, heavy-bottomed pot with a lid, heat the oil over medium heat until it shimmers, about two minutes. Add the leeks and carrot and cook, stirring occasionally, until the carrots begin to soften and brown, about five minutes. Add the garlic and cook, stirring constantly, until fragrant, about 30 seconds. Add the stock, bay leaves, lemon zest, salt, pepper, and chicken. Bring to a boil over medium-high heat, then reduce the heat to low, cover, and let simmer until the chicken is fully cooked, about 15 minutes. Remove and discard the bay leaves. Transfer the chicken to a cutting board and, using two forks, shred it.

Add the couscous to the pot and stir until incorporated. Cover and cook until the soup has thickened, about 10 minutes. Uncover and stir in the shredded chicken.

In a small bowl, whisk together the egg and lemon juice until smooth. While whisking constantly, slowly add one ladle of simmering broth to the egg mixture to temper it.

Add the tempered egg mixture to the soup and stir to incorporate. Remove the pot from the heat. Ladle into soup bowls and garnish with dill.