Place apples and raspberries in the rice cooker; add brown sugar, cinnamon, and nutmeg. Add honey, vanilla extract, lemon juice, and water, in respective order.
Set rice cooker to standard "cook" setting, about 30 minutes. Stir mixture halfway through cooking cycle, mashing apples a little bit.
Remove the applesauce from the heat and cool for 30 minutes. Transfer applesauce to a bowl and chill in the refrigerator for at least 1 hour.