Rinse the mung beans in cold water until the water runs clear. Set aside.
Heat a large pot or deep skillet over medium-high heat. Add oil, and once it starts shimmering, add onions, garlic, and ginger. Cook for 4 minutes until the onions are translucent.
Add cumin, coriander, turmeric, cayenne pepper, and salt. Cook for 30 to 60 seconds until fragrant, stirring frequently to prevent burning.
Add 3 cups of water, dried mung beans, and crushed tomatoes. Reduce heat to low, cover with a lid, and simmer for 35 minutes until the mung beans are mostly softened. If they're not quite soft after 35 minutes, add a few spoons of water and cook for an additional 5 minutes.
Remove the lid. Stir in coconut milk and butter. Continue cooking on low heat, uncovered, for 10 minutes until the curry thickens and becomes creamy. Stir in lemon juice and cilantro, then serve.
