Melt the ghee in a large heavy-bottomed pot over medium heat. Add the onion and season generously with salt and pepper, then add the turmeric, cumin, and cayenne. Cook, stirring, until the onion is softened, about 10 minutes. Add the lentils and water and bring slowly to a boil. Skim and discard any rising foam—there may be a lot—and stir diligently, because sometimes the mixture can overflow the pot during the first few minutes of cooking.
Turn the heat down to low, partially cover the pot, and simmer gently for about 45 minutes, until the lentils are quite soft. When the lentils are cooked, taste and adjust the salt. For a smooth, velvety consistency, puree the dal in a blender, then return to the pot. Or, if you prefer some texture, just beat with a whisk for a minute or two. If the dal is very thick, thin with a little water. (I prefer it on the soupy side.)