Prick the squash skin with a fork and place in the microwave on high for about 3 minutes. Remove from the microwave and let cool for a few minutes. Cut the squashes in half and place the cut sides down in a baking dish for about 40 minutes. Check for doneness by piercing with a fork; there should be little resistance.
Scoop the squash flesh from the skin into a bowl and mash with a potato masher or fork, or use a food mill.
Add the lemon juice and stir well. Add the cinnamon, brown sugar, and nutmeg, to taste.