Cook the lentils - Rinse the lentils and place them in a large pot. Cover with water and bring to a boil. Reduce heat and simmer for 20-25 minutes or until the lentils are tender.
Sauté onions and garlic - While the lentils are cooking, heat a large pot over medium heat. Add a splash of olive oil and sauté the onions and garlic until they become fragrant and translucent, about 5-7 minutes.
Add curry powder and turmeric - Add curry powder and turmeric to the pot with onions and garlic and stir for a minute or so to let the flavors bloom.
Add the vegetables and vegetable broth - Add the diced carrots and tomatoes to the pot, followed by the vegetable broth. Bring to a boil and then reduce heat to a simmer. Let the soup cook for 10-15 minutes, or until the vegetables are tender.
Add the coconut milk, spinach, and lime juice - Add the coconut milk and spinach to the pot and stir until the spinach has wilted. Finally, squeeze in the lime juice and stir to combine.
Season and serve - Taste the soup and adjust seasoning as needed with salt and pepper. Ladle into bowls and serve hot. Top with additional lime juice, cilantro, or chili flakes as desired.