Combine blueberries, lemon juice, cinnamon, 4 tablespoons sugar, and salt in a medium saucepan and bring to a boil over high heat. Reduce heat and simmer until blueberries burst and become very soft, about 8 minutes. Transfer mixture to a food processor and puree. Pour into a fine sieve set over a bowl, stirring and pressing on solids to remove as much liquid as possible. Discard solids and refrigerate puree until cold and thickened slightly, at least 1 hour and, covered with plastic wrap, up to 1 day.