Add chicken and broth. Bring to a boil, then reduce heat to a maintain a simmer. Cook until an instant-read thermometer inserted in the thickest part of the chicken registers 165 degrees F, 10 to 12 minutes. Remove from heat; transfer the chicken to a plate to cool slightly. When cool enough to handle, shred or chop the chicken and return it to the soup. Stir in the cooked orzo, along with lemon juice, dill, salt, and pepper.