Wash the split red lentils in a colander until the water runs clear. Soak them covered in water for atleast 30 mins. Discard soaking water when ready to cook.
Once soaked, add the green chilli, salt, water and turmeric powder to the lentils. Bring the pot to a boil on a medium flame. If you see any foamy impurities, skim them out.
Once the lentils have come to a boil, reduce the heat to a gentle simmer. Using the back of a spoon, gently mash some of the lentils to make the final dal creamy. Its important not to over-cook the dal - you till want some texture.
Now, add the chopped tomato and let it cook until softened slightly. Add the sugar and adjust seasoning if necessary.
For the tempering - heat the ghee (use a neutral oil if you'd like to make this vegan). Add the mustard seeds, let them bloom and splutter in the oil on a low flame. Turn off the heat and immediately add the heeng (asafoetida) and the curry leaves and quickly pour this tempering to the dal and mix through nicely and turn off the heat.
Add the lime juice and taste the dal for balance. Garnish with coriander leaves and let it rest for about 15-20 minutes before you serve.
Serve your dal with some steamed rice, a side of vegetables or greens and some yogurt.