Place the chicken thighs in the slow cooker. Add the minced garlic, lemon zest, lemon juice, chicken broth, sliced carrots, sliced celery, diced onion, dried thyme, salt, and black pepper.
Cover and cook on low for 6 hours until the chicken is very tender.
Remove the chicken to a plate and shred it with two forks. Return the shredded chicken to the slow cooker and stir to combine.
In a mixing bowl, stir together the flour, baking powder, and milk with the melted butter to form a thick dumpling batter.
Drop spoonfuls of the batter directly onto the hot broth in the slow cooker. Cover and cook on high for 1 hour until the dumplings are cooked through and no longer doughy in the center.