Cut each lemon into a few chunks and toss with sugar in a large glass, ceramic, or stainless steel mixing bowl. Cover tightly and let stand at room temperature, stirring once every 45 minutes or so, until sugar has completely dissolved, about 3 hours (or up to 12 if timing is an issue).
Using a cheesecloth-lined or fine-mesh stainless steel strainer set over a nonreactive bowl, strain syrup. Working in batches, transfer rinds to a stainless steel potato ricer and squeeze to release any extra syrup, allowing it to pass through strainer into bowl; discard rinds. Refrigerate syrup for up to 3 months in a glass bottle or pint jar.