Beat the eggs and lemon juice in a bowl. 

Heat the oil in a saucepan over medium-high heat.

Add the carrots and onion.

Cook, stirring for 5 minutes. 

Add the broth and bring to a simmer. Add the orzo and simmer for 5 minutes. 

Ladle some of the broth into the bowl with the eggs and whisk to temper them. 

Pour the tempered eggs into the broth in the pot and stir to combine.

Add the chicken and spinach and cook until the spinach is wilted. 

Season the soup to taste with salt and pepper and add dill. 

Ladle soup into the bowls and serve.