Season the chicken thighs all over with salt & pepper.
Heat the oil in a dutch oven or large pot over medium-high heat until very hot.
Sear the chicken thighs, skin-side down, until browned, about 3 minutes.
Transfer the chicken thighs to a plate and set aside.
Add the carrots, celery, onion, ginger, and garlic to the pot and cook, stirring often, until the vegetables have softened a bit, about 3 minutes.
Return the chicken to the pot along with the water and 1 tsp salt then bring to a boil.
Reduce the heat to medium-low then place a lid on the pot and cook, stirring occasionally, until chicken is very tender, about 45 minutes.
Transfer the chicken to a plate then shred the chicken, discarding the skin and bones.
Stir the shredded chicken back into the pot then return the heat to medium-high and bring to a boil.
Add the pasta to the pot then reduce the heat back to medium-low and continue to cook, stirring occasionally, until the pasta is tender, 5 to 10 minutes.
Stir in the lemon juice then taste and season the soup with additional salt & pepper as needed.
Serve the soup in bowls topped with the sliced green onion.