Measure out and strain the fresh lemon juice through a fine sieve into a mixing bowl to remove pulp and seeds.
Combine the lemon juice and sugar in a saucepan and gently heat over medium-low, stirring constantly until the sugar dissolves completely and the mixture is warm (about 3-4 minutes). Look for a clear, slightly steaming liquid without granules.
In a separate bowl, lightly whisk the eggs until well combined, then slowly pour a small amount of the warm lemon mixture into the eggs while stirring constantly to temper them (about 2 tablespoons). This prevents curdling.
Gradually pour the tempered eggs back into the saucepan with the remaining lemon mixture, whisking continuously. Increase heat slightly and cook, stirring constantly, until the mixture thickens and coats the back of a spoon (about 5-7 minutes). You should see a slight glossy sheen and thickening texture.
Remove the saucepan from heat and stir in the butter and lemon zest until smooth and fully incorporated. The mixture should be silky and glossy.
Pour the hot pudding through a fine sieve into serving bowls or ramekins to ensure a smooth final texture. Cover and refrigerate for at least 2 hours before serving to allow the pudding to set slightly and chill thoroughly.
