Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 5 minutes.
Stir in the garlic, ginger, cumin seeds, turmeric, garam masala, and cayenne pepper. Cook for 1 minute until the spices smell fragrant.
Add the brown lentils, turnip cubes, and sweet potato cubes to the pot. Pour in the vegetable broth and stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 25 to 30 minutes until the lentils are tender and the vegetables are cooked through.
Season with salt and black pepper. Taste and adjust the seasoning if needed.
Ladle the stew into bowls. Top each serving with chopped cilantro and serve with lemon wedges on the side.