You can dry roast the dal instead of doing it in ghee.
I used karupatti/ palm jaggery in this recipe. You can use any type of jaggery as per your wish.
Ensure to cook the dal along with the thin coconut milks for sufficient time so that the dal gets cooked thoroughly. You need a bit of patience for this. Otherwise, when you serve, you will have the liquid on the top and the dal at the bottom of the pitcher, which is not a very interesting scene! Cook on low flame till you feel satisfied with the thickening.
As it cools, it tends to thicken. Add a bit of warm water to loosen up.
You can use fresh coconut milk. However, I resorted to the easier way of making it with coconut milk powder - for moonnaam paal, I used 1 tsp in 1 cup of water, for randaam paal, I used 1 tsp in 3/4 cup water and for the onnaam paal, I used 1 heaped tsp in 1/2 cup of water.