Peel, core and coarsely chop apples. Place in a saucepot with water or apple juice and bring to a boil. Reduce heat and simmer, partially covered, until apples are tender, 15-30 minutes, depending on the variety of apple and size of chunks. When apples are cooked mash if smoother consistency is desired. Add lemon juice if apples were bland or too sweet. Add sweetener and cinnamon to taste if desired. Serve warm or cold.