Instructions

Combine quinces and water in Dutch oven and place parchment paper round over surface to keep fruit submerged. Bring to boil over high heat. Cover, reduce heat to medium-low, and simmer until quinces are very soft and can be easily pierced with knife, about 1½ hours. Drain quinces in colander set in large bowl, reserving liquid (it should measure about 5 cups).
Return reserved liquid to pot and bring to boil over medium-high heat. Boil until reduced to 3 cups, 12 to 15 minutes. While liquid boils, process quinces in food processor until very smooth, about 45 seconds, scraping down sides of bowl as needed. Working in small batches, pass quince puree through fine-mesh strainer set over medium bowl; discard solids (you should have about 4 cups puree).
Adjust oven rack to middle position and heat oven to 350 degrees. Grease 8-inch square baking pan, line with parchment, and set aside. Add puree to reduced liquid in pot. Stir in sugar and lemon juice and bring to boil. Reduce heat to medium-low and simmer, stirring occasionally, until puree darkens, becomes very thick, and begins to spatter, about 30 minutes.
Transfer pot to oven and cook until puree turns dark rusty brown and is thickened and rubber spatula leaves distinct train when dragged across bottom of pot, 1 to 1½ hours, stirring and scraping sides of pot every 15 minutes. Transfer to prepared pan, smooth top, and let cool completely. Refrigerate until set and firm, at least 4 hours.