In a large saucepan, combine the cranberries, sugar, water and salt and bring to a boil. Simmer over moderately low heat, stirring, until the sugar dissolves and the mixture is bright red, 8 to 10 minutes.
Strain the syrup through a fine sieve set over a heatproof bowl, without pressing; reserve the solids for another use. Stir in the lemon juice. Let the syrup cool completely, then funnel it into glass bottles and refrigerate until chilled, about 1 hour. Shake before serving.