Coarsely grate the lemon rinds, juice the lemons, and combine with the basic syrup in a pan.
Cook at a slow boil for 10 minutes, covered. It may be cooked longer, uncovered, to intensify the flavor. Let stand overnight, covered. Strain, reboil, and seal in sterile jars or refrigerate. When stored in the refrigerator, there is no need to reboil the syrup but it