Rinse the three types of lentils separately until water runs clear. Soak each daal for 1.5 hours. Drain water. Mix three types of soaked daal together. Set aside.
Melt ghee over medium heat in a large, heavy-bottomed pot. Fry cumin seeds in ghee until they splutter. Sprinkle asafoetida powder. Stir briskly. Add onion and fry until translucent, stirring frequently. Add ginger and garlic. Stir and fry until the raw garlic smell disappears, about 3 minutes.
Add turmeric and ground coriander. Stir and fry until the spices release their aroma, about 1 minute.
Add lentils, crushed tomatoes, water and 1 tbsp salt. Stir well.
Bring mixture to a boil. Reduce heat to medium. Watch carefully for the first 10-15 minutes. You need to skim the scum that comes to the top. Try not to stir the mixture too vigorously for the first 15 minutes. Stirring re-incorporates scum. Only stir to prevent lentils from sticking to the bottom of the pot. Stir well and cover the pot. Cook. Stirring occasionally, for 1 hour.
Uncover. Add the chopped green chili. Cook, uncovered, for about 30 minutes. The daal is done when all of the masoor daal have disintegrated and only the chenna daal hold their shape.
Stir in the lemon juice and aamchur powder. Adjust salt to taste.
Stir in the chopped cilantro right before serving. Garnish with extra chopped cilantro, diced tomato and green chili. Serve with basmati rice or rotis.