Trim ends from oranges and lemon and discard. Cut citrus into 2-in. chunks, discarding seeds. Peel and core apples and cut into 2-in. chunks.
Pulse fruit chunks and cranberries in batches in a food processor until coarsely chopped; pour into a bowl. Stir in sugar to taste. Add almonds up to 2 hours before serving.
Make ahead: Chill up to 1 week.
Note: Nutritional analysis is per serving.