Heat oil in a medium pot over medium-high. Add onion and cook, stirring occasionally, until softened and lightly browned around the edges, 5–7 minutes. Add ginger and garlic and cook, stirring often, just to take the edge off garlic, about 30 seconds. Add ⅓ cup water and simmer, stirring occasionally, until water evaporates about 1 minute. Add the lentils, coriander, turmeric, cardamom, and red pepper flakes and cook, stirring, until fragrant, about 30 seconds.
Add 4 cups water and bring to a boil. Reduce heat to medium-low and simmer, stirring occasionally, until the lentils are very tender and most of the liquid is absorbed, 20-25 minutes; season with salt and black pepper to taste. Cover with a lid and keep dal warm over low heat while you make the toppings.
Finely grate the zest from lime into a small bowl. Cut lime in half and squeeze juice into a bowl (approximately 2 tablespoons). Add red onion, sugar, and a large pinch of salt and toss, squeezing onion with your hands to help it soften quickly.
Mix Cashewmilk Yogurt and 2 Tbsp. water in a small bowl; season with salt.
Serve daal over rice and top with the Cashewmilk Yogurt and pickled onions.