Combine water, chana dal, turmeric, and salt in a multi-functional pressure cooker (such as Instant Pot(R)). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 20 minutes. Allow 10 to 15 minutes for pressure to build.
While chana dal is cooking, heat coconut oil in a skillet over medium heat until shimmering, about 2 minutes. Add onion and cook 30 seconds. Add ginger and garlic; cook 5 minutes. Add tomatoes, cumin, salt, and cayenne. Cook and stir for 30 to 60 seconds. Add water and stir to remove browned bits from the bottom of the skillet. Cook 2 minutes more.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and remove the lid. Chana dal should be soft enough to be easily crushed by a spoon.
Transfer 1/3 to 1/2 of the cooked dal into the skillet with the onion mixture. Use an immersion blender to process until pureed. Mix in remaining dal and cook until heated through, 3 to 5 minutes more.
