Bring quinces, sugar, and 4 cups water to a boil in a medium stockpot. Reduce heat. Place a lid from a slightly smaller pot over fruit to keep submerged, and simmer until liquid is pale pink and has been reduced to a thin syrup, about 1 hour 10 minutes. Strain; reserve cooked quinces for stuffing. Stir in lemon juice.
Syrup can be refrigerated in an airtight container for up to 1 week.