Place apple in a large bowl; cover with cold water. Squeeze juice from lemon half into bowl; place lemon half in bowl. Set aside.
Combine cranberries and remaining ingredients in a Dutch oven; bring to a boil, stirring occasionally. Cook 3 minutes or until cranberries pop.
Drain apple; discard lemon. Add apple to pan. Cover, reduce heat, and simmer 25 minutes or until apple is soft. Uncover, bring to a boil, and cook 15 minutes. Mash apple mixture with a potato masher. Pour into serving dish; cover and chill at least 2 hours.