Rinse the lemons under plain running water, rubbing the skins well. Dry completely so no water dilutes the alcohol infusion.

Use a vegetable peeler to take off thin strips of yellow zest. Trim away any thick white pith with a paring knife; pith makes the liqueur bitter.

Put the peels in a clean 2-quart glass jar and pour in the vodka. Seal tightly and store in a cool, dark cupboard for 7 days. Swirl the jar gently once a day.

After 7 days, the liquid should be deep yellow and strongly fragrant while the peels look noticeably paler. Infuse up to 14 days for a more intense flavor, tasting a drop after day 7.

Combine the sugar and water in a saucepan. Warm over medium heat, stirring, until completely dissolved, about 5 minutes. Do not boil hard. Cool the syrup fully to room temperature.

Strain the lemon vodka through a fine-mesh strainer; pass it through a coffee filter if you want a clearer finish. Discard the peels. Stir in the cooled syrup. The mixture may turn cloudy, which is normal.

Pour into clean bottles, seal, and rest for at least 24 hours in the refrigerator. Serve chilled in 1-ounce pours. Store tightly sealed in the refrigerator or freezer.