Heat the olive oil in a large pot over medium heat. Add the onion, garlic, and ginger and cook for 3 to 4 minutes until the onion softens.
Stir in the curry powder and cook for 30 seconds until fragrant.
Add the red lentils, vegetable broth, coconut milk, and carrots. Bring the mixture to a boil, then reduce the heat and simmer for 20 minutes until the lentils are tender.
Stir in the spinach and cook for 2 more minutes until it wilts.
Season with salt and black pepper. Serve the soup with fresh cilantro and lime wedges on the side.