In a medium-size mixing bowl, combine the egg yolks, cornstarch, and 1 cup of the heavy cream. Whisk to blend well. Set aside.
Combine 2 cups of the heavy cream, the lemon juice and sugar in a large heavy non-reactive saucepan over medium heat. Whisk to dissolve the sugar and bring to a gentle boil. Slowly add the egg mixture, whisking constantly as it thickens, about 5 minutes. Be forewarned, the mixture will break. Don't be alarmed. Pour it into a glass bowl and press a piece of plastic wrap down over the surface to prevent a skin from forming. Let cool completely to room temperature. When cooled, pour the mixture into a medium-size mixing bowl. With an electric mixer fitted with a wire whip, beat at medium speed to recombine. If it doesn't warm another 1/2 cup heavy cream and slowly add it to the mixture. Whip until you have a thick and creamy custard.