Heat oil in a medium pot over medium-high. Add onion, season with salt, and cook, stirring occasionally, until golden brown and caramelized, 12–15 minutes. Add garlic and cook, stirring often, until garlic is golden and onion is deep golden brown, about 5 minutes. Remove pot from heat and transfer onion and garlic to a plate; set aside for serving.

Return pot to medium-high heat; pour in lentils and sprinkle turmeric over. Cook, stirring a few times, until fragrant, about 30 seconds. Add chicken and 6 cups water; season with salt and some pepper. Bring to a simmer over medium-high heat. Reduce heat to medium-low; cook, stirring occasionally, until lentils are tender, 20–25 minutes.

Remove from heat and stir in dill and lemon juice.

Ladle soup into bowls; drizzle with yogurt and top with reserved onion mixture, dividing evenly.