Rinse the lentils under cold water for 30 seconds and pick out any stones. Dice the onion, carrots, and celery into 1/2-inch pieces, mince the garlic, chop the parsley, juice the lemon, and pat the chicken thighs dry.
Season the chicken with 1 teaspoon salt and 1/4 teaspoon pepper. Heat 1 tablespoon olive oil in a Dutch oven over medium-high heat and sear the chicken for 3 to 4 minutes per side until golden brown. Transfer to a plate, keeping any juices.
Reduce heat to medium and add the remaining olive oil, onion, carrots, and celery. Cook for 6 to 8 minutes, stirring often and scraping up browned bits, until the onion is soft and translucent.
Push the vegetables to the sides and stir in the garlic, tomato paste, cumin, thyme, and smoked paprika. Cook for about 1 minute, stirring constantly, until darkened and fragrant.
Stir in the lentils, then pour in the broth and diced tomatoes with their juices. Add the bay leaves, nestle the chicken into the liquid with any juices, and bring to a boil.
Reduce heat to low, partially cover, and simmer for 30 to 35 minutes until the lentils are tender but still hold their shape and the chicken reaches 165°F. Add hot water or broth if too thick.
Discard the bay leaves, lift the chicken onto a cutting board, and shred it with two forks. Return the shredded chicken to the pot and stir in the baby spinach until wilted, about 2 to 3 minutes.
Stir in the lemon juice, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. Taste and adjust with more salt or lemon juice, then ladle into warm bowls and sprinkle with fresh parsley.