Place strawberries in a blender or food processor and pulse until puree is smooth. Transfer to a bowl and add salt, lemon juice, sugar and mix.
Transfer the strawberry mixture to a blender and purée with cream until smooth. Return strawberry cream to bowl and chill, stirring occasionally, until very cold, 3 to 6 hours. (Note: you could halve this time if you placed it in the freezer for an hour, stirring it every 15-20 minutes.)
Freeze mixture in ice cream maker. Transfer to an airtight container, place a plastic wrap on the surface, cover and put in freezer to firm up.