Combine the sugar, butter and lemon juice in a small saucepan over medium-low heat. Cook just until the butter melts. Whisk in the eggs. Cook, stirring frequently with a rubber spatula, until the mixture thickens and coats the back of a spoon, 6-8 minutes. Do not let the mixture bubble. Pour then press through a fine-mesh strainer into a bowl. Press plastic wrap over top and let cool to room temperature. Refrigerate until set, about 2 hours.