In a large soup pot, combine the broth and water. Cover and bring it to a boil on high heat.
Add the orzo and cook al dente according to package directions, stirring occasionally. Reduce heat to low.
Meanwhile, in a large bowl, beat the eggs until smooth. Gradually whisk in the lemon juice until incorporated. Slowly whisk ⅓ cup of the hot broth into eggs.
Slowly stir egg mixture into remaining broth. Add the shredded chicken. Cook 2-3 minutes, until thickened, stirring occasionally. Season with salt and pepper if necessary.
For extra flavor, garnish with thin lemon slices and chopped fresh dill or dried dill.