Place the sliced plums, sugar, lemon juice, and salt in a blender and purée until very smooth. Push the plum puree through a fine mesh sieve to catch and large pieces of skin and discard them.
Mix the Grand Marnier to the purée just before churning. Place the purée in an ice cream machine and churn according to instructions, for approximately 25 minutes. Serve immediately or place in an air tight container and put in the freezer for two hours to firm up.