Combine sugar, 1 1/2 cups water, and plums in a small pot and bring to a simmer, stirring, until sugar is dissolved. Remove from heat and let cool completely. Pass through a fine sieve into a bowl, pressing on solids to extract as much liquid as possible.
Stir lemon juice, rose water, and salt into sugar syrup. Refrigerate until well chilled, at least 2 hours and up to overnight. Stir well, then freeze in an ice cream maker according to manufacturer's instructions. Store in freezer in a metal loaf pan, covered with plastic wrap, until ready to serve, up to 2 days.