Combine pineapple, sugar, water, honey, and lemon juice in a medium saucepan. Bring to a boil; reduce heat, and simmer 3 minutes. Remove from heat, and let cool. Pour pineapple mixture into a 2-quart jar; add rum, stirring well. Cover tightly, and store in a dark place at room temperature at least 2 weeks. Shake jar gently once daily.
Pour pineapple mixture through a wire-mesh strainer into a large bowl, discarding pineapple. Add condensed milk, and stir mixture with a wire whisk. Pour mixture into jars, and cover tightly. Store in refrigerator.
Use in beverages, or serve over commercial low-fat pound cake, nonfat frozen yogurt, fresh pineapple, banana slices, or strawberries.