Heat the oil in a dutch oven or large pot over medium heat.
Season the chicken thighs all over with salt & pepper then place the chicken skin-side down in the hot oil and cook until skin is browned, about 8 minutes.
Transfer the chicken to a plate and set aside leaving any oil and fat in the dutch oven.
Add the farro, carrots, celery, onion, 1 tsp salt, and 1/2 tsp black pepper to the pot and cook, stirring often, for about 5 minutes.
Pour the water into the pot with the vegetables then put the chicken back into the pot and bring to a boil over medium-high heat.
When soup begins to boil place a lid on the pot and reduce the heat to medium-low.
Simmer the soup until chicken is cooked through and tender, about 40 minutes.
Take the soup off the heat then transfer the chicken to a plate. Use two forks to shred the chicken meat, discarding the skin and bones.
Stir the shredded chicken into the soup along with the lemon juice and zest.
Taste soup and season with additional salt & pepper as needed.