Heat the olive oil in a large pot over medium heat. Add the diced onion and cook until it softens, about 4 minutes.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the Thai red curry paste and stir to coat the onion mixture.
Pour in the rinsed brown lentils, coconut milk, diced tomatoes, and vegetable broth. Stir well to combine.
Bring the mixture to a simmer, then reduce the heat and cook uncovered for 25 minutes, stirring occasionally, until the lentils are tender.
Add the fresh spinach and stir until it wilts, about 2 minutes.
Season with salt and pepper to taste. Serve hot, topped with chopped cilantro and a squeeze of lime.