Heat 2 tablespoons oil in a large saucepan or medium Dutch oven over medium heat. Add chopped onion, minced garlic and cut ginger; cook, stirring often, until the onion softens and starts to brown, 6 to 8 minutes. Add 1 bay leaf, 1 teaspoon turmeric, ½ teaspoon each coriander and salt and ¼ teaspoon pepper; cook, stirring constantly, until fragrant, about 1 minute. Add trimmed chicken, 5 cups broth and sliced sweet potatoes; bring to a vigorous simmer over high heat.  Reduce heat to medium-low and simmer, stirring occasionally, until the sweet potatoes are tender but not falling apart, and an instant-read thermometer inserted into the thickest portion of chicken reads at least 165°F, 15 to 18 minutes.

Transfer the chicken to a plate to cool slightly, about 5 minutes. Remove and discard the bay leaf. Meanwhile, add 5 cups kale to the soup; cook, stirring constantly, until just wilted, about 1 minute. Remove from heat.

Remove and discard skin and bones from the chicken; shred the chicken. Stir 2 tablespoons lemon juice and the shredded chicken into the soup. Season with additional lemon juice to taste.