Core apples. Peel about 1/3 down the apple. Stand apples up in a large ceramic or glass pie plate and make 4 evenly spaced vertical cuts starting from top of each apple and stopping halfway from bottom to keep apple intact. Brush inside and outside of peeled apple with lemon juice.
Toss together apricots, pecans, brown sugar, cinnamon, and nutmeg in a bowl. Rub softened butter into dried fruit mixture with your fingers until combined well. Pack center of each apple with mixture. Put a piece of the remaining butter on top of each apple. Pour cider around apples and cover pie plate tightly with foil.
Bake in middle of oven, basting once, until apples are just tender when pierced with a fork, about 45 minutes. Remove foil and continue to bake until apples are very tender but not falling apart, 20-30 minutes more.
Transfer to serving dishes and spoon sauce over and around apples.