Season chicken thighs with salt and pepper. Heat oil in a large pot over medium-high. Sear thighs skin-side down for 5 minutes, then flip and sear 2 more minutes. Remove to a plate.

Reduce heat to medium. Add onion, carrots, celery, and garlic. Cook 5 minutes, scraping up browned bits.

Pour in broth, dill, bay leaf, and return chicken. Bring to a boil, then simmer covered for 25–30 minutes.

Transfer chicken to a board; let cool slightly. Shred meat, discarding bones and skin, and return to pot.

Stir in rice and simmer uncovered for 12–15 minutes, until rice is tender. Remove from heat, stir in lemon juice, and season to taste. Ladle into bowls, top with fresh dill, and serve.