Add a swirl of oil to a medium pot. Heat over medium-high flame until shimmering. Add the onion, and sauté until slightly softened, 1 to 2 minutes.
Add the garlic and ginger, sautéing until fragrant and barely golden, about 1 minute.
Stir in the tomato paste. Add the curry, turmeric, red pepper flakes, and season with salt and pepper.
Stir in the coconut milk and vegetable broth. Add the lentils. Bring to a boil. Reduce flame to a simmer, and cooking until the lentils are very tender, and broken down, 25 to 30 minutes. The soup will be thick, and the lentils broken down a bit. Serve hot, topped with cilantro and a squeeze of lime.
Note for leftovers: The soup thickens as it cools, so you might want to add a little more coconut milk or broth when reheating.