Preheat oven to 200 degrees. Generously coat two 13-by-9-inch rimmed baking sheets with cooking spray, and line with a Silpat baking mat if desired.
Working in batches, puree apples, cranberries, apple juice or cider, lemon juice, honey, and sugar in a blender. Pour into a bowl to combine.
Divide puree between prepared pans. Let stand 1 minute, then drain excess liquid. Smooth with an offset spatula. (The puree should be almost 1/4 inch thick.) Bake, with oven door open slightly, until dry to the touch (but not browned), about 6 hours. Close oven door, turn off oven, and let dry overnight in the oven. (Fruit leather should be stiff, but still pliable.)
Remove fruit leather from pans. Trim uneven edges, cut into desired size, and roll up if desired. Fruit leather can be wrapped in plastic and refrigerated in an airtight container for up to 1 month.