1. In a large bowl, combine strawberries, 1/4 cup of the sugar, and lemon juice. Crush with a potato masher until strawberries are almost completely pureed (or pulse in a blender or food processor). Set aside.
2. In a 2-quart saucepan, bring half-and-half cream and remaining sugar to a boil over high heat. In a medium bowl, combine egg yolks and salt. Pour 1/2 cup of the hot half-and-half mixture into the egg yolks, beating with a wire whisk the whole time.
3. Pour this mixture back into the saucepan and cook over medium heat, stirring constantly with a rubber spatula just until mixture coats the back of the spatula, about 1 to 2 minutes. Do not let mixture come to a boil. Remove from heat and stir in heavy cream and vanilla. Let mixture cool completely, about 15 minutes. Stir in strawberry mixture. Transfer mixture to ice cream maker and freeze according to manufacturer's directions. Makes 5 cups.