In a large metal bowl or the top of a double boiler, combine lemon juice, butter, eggs, and sugar. Set the bowl over a saucepan of simmering water; whisk until butter melts, sugar dissolves, and the mixture thickens, about 15 minutes. Allow the lemon curd to cool slightly, and stir in the extract, cream, and salt. Cover and refrigerate until cold or overnight.
Stir the cold custard well, then freeze in your ice cream machine according to manufacturer’s instructions. When finished, the ice cream will be soft, like soft serve. For firmer ice cream, freezer at least 2 hours.