Combine cranberries and water to cover in a heavy saucepan. Bring to a boil. Reduce heat; cover and simmer 15 minutes. Drain and cool. Process cranberries through a food mill. Discard pulp, and reserve puree.
Soften gelatin in 1/4 cup water.
Combine cranberry puree, remaining water, sugar, and salt in a heavy saucepan. Bring to a boil, stirring constantly. Remove from heat; stir in softened gelatin and lemon juice. Cool.
Pour into a 2-cup metal ice tray (with divider removed); freeze for several hours, stirring 2 to 3 times during freezing process until mixture reaches the consistency of a sherbet.
Scoop into sherbet dishes; serve immediately.