Preheat oven to 350 degrees. Place the barley on a baking sheet and roast for 10 to 15 minutes. While the barley is roasting, prep your ingredients.
If the chicken thighs have skin, pull it off and discard. Peel and dice the carrots. Dice the celery. For the leeks, cut away the end root and the dark green top, leaving only the white and pale green parts. Cut in half vertically and then cut those in half vertically as well. Thinly slice the leeks on the horizontal. You should have 2.5 cups. Peel the ginger and grate it on a micro plane.
Add everything except the lemon juice to a slow cooker. Cover and cook for 3 hours and 30 minutes on low. Take the chicken out and debone the chicken. Shred or chop it into bite sized pieces and put it back in the slow cooker. Add the lemon juice, stir, and cover. Cook for 30 more minutes. Add salt and pepper to taste.