Beat egg whites in a bowl using an electric mixer until soft peaks form. Add 1/4 cup sugar slowly, beating batter until peaks stiffen.
Combine water, the remaining 1/4 cup sugar, and salt in a bowl. Stir until sugar and salt are dissolved. Stir in cream and lemon juice until just combined. Fold in the beaten egg whites. Pour mixture into an ice cream maker and freeze according to manufacturer's instructions, about 20 minutes. Transfer to an airtight container and freeze until firm, about 1 hour.