Bring chicken stock and lentils to a boil in a large saucepan over high heat. Reduce heat to medium-low, cover, and simmer for 20 minutes.
Meanwhile, heat olive oil in a skillet over medium heat. Stir in onion and garlic; cook until onion has softened and turned translucent, about 3 minutes.
Stir onion mixture into lentils; season with cumin and cayenne. Continue simmering until lentils are tender, about 10 minutes.
Purée soup in a standing blender or with a stick blender until smooth. Stir in lemon juice and cilantro.