Bring the chicken broth to a boil in a large heavy-bottomed pot over medium-high heat.
Add the rice to the boiling broth, then reduce heat to low, cover, and simmer for 15 to 18 minutes until the rice is tender.
In a medium mixing bowl, whisk the eggs until frothy and well-combined, then slowly whisk in the lemon juice.
Temper the egg mixture by slowly drizzling in 1 cup of the hot broth while whisking vigorously to prevent curdling.
Pour the tempered egg mixture back into the main pot with the remaining broth and rice, stirring constantly over low heat.
Add the shredded chicken, salt, and pepper; continue stirring until the soup thickens slightly and is heated through, ensuring the liquid does not reach a boil.
Remove from heat and serve immediately garnished with fresh dill.