Peel and seed satsumas, reserving peels. In the work bowl of a food processor, process satsuma flesh and peels and lemon zest and juice until almost smooth, about 1 minute. (There should still be some small pieces remaining.)

In a medium saucepan, bring satsuma mixture to a boil over medium heat. Reduce heat to low, and simmer for 10 minutes. Stir in sugar and salt, and increase heat to medium-high; cook, stirring frequently, until mixture is thickened and an instant-read thermometer registers 210°F (98°C), 35 to 40 minutes. Remove from heat, and let cool completely. Refrigerate in an airtight container for up to 1 month.