Preheat oven to 425°F Place squash, onion, and chicken on a baking sheet in a single even layer. Drizzle with olive oil, and sprinkle with salt, and pepper. Toss to coat and roast until the chicken is cooked through and squash is tender, about 30 minutes.
Transfer chicken to a plate. When cool enough to handle, remove and discard skin, and tear chicken into bite-sized pieces. Set aside.
Meanwhile, place cooked squash and onion in a soup pot with chicken broth. Add the cumin and coriander and bring to a simmer. With a potato masher or wooden spoon, mash up the soup, leaving some chunks of squash. Stir in lemon juice. Return chicken to soup and simmer until heated through. Adjust salt, pepper and lemon if needed. Serve with cilantro for garnish.