Heat oil in a large pot over medium heat. Add the onion and carrot. Sauté the vegetables until the onion is soft and clear, about 5 minutes. Add the garlic and continue to cook, stirring frequently, for another 2 minutes. Add a few tablespoons water to the pot to help prevent sticking if necessary.
Add the lentils, sweet potato, turmeric, garam masala, curry powder, salt, and pepper. Stir to combine everything. Add the broth and bring to a boil. Reduce to a simmer and cook for twenty-five minutes, or until the lentils and sweet potato are tender. Stir in the 1/2 cup coconut milk and lime juice. Serve.
Curry will keep for up to four days in the fridge. Leftovers can be frozen.
Notes
Leftover curry will keep for up to 5 days in an airtight container in the fridge. They can be frozen for up to 1 month.