Keep this jam in the refrigerator up to 1 month.
Stir together fruit and sugar in a 4 1/2-qt. saucepan. Let stand 10 minutes. Meanwhile, zest 1 lemon to equal 1 tsp. Cut lemon in half; squeeze juice from lemon into a bowl to equal 2 tsp. Peel and section second lemon, removing seeds and chopping segments.
Stir pectin and, if desired, ginger, into fruit mixture, and bring to a rolling boil over medium heat, stirring often. Boil, stirring constantly, 5 minutes. Reduce heat to low; stir in lemon zest, chopped segments, and lemon juice. Cook, stirring occasionally, 3 minutes; remove from heat. Cool 10 minutes.
Pour jam into 2 (8-oz.) canning jars, and cool completely (about 30 minutes). Cover with lids, and refrigerate up to 1 month.