Whisk the sugar, lemon zest, and lemon juice in a medium saucepan. Whisk in the whole eggs and yolks in a small bowl and then whisk them into the lemon mixture.
Cook the mixture over medium-low heat, whisking constantly, until it's thick like pudding, about 6 to 8 minutes. Remove from the heat and whisk in the butter, a few pieces at a time until incorporated.
Strain the mixture through a fine-mesh sieve into a small bowl, pushing it through with a rubber spatula. Press plastic wrap directly onto the surface to prevent a skin from forming. Refrigerate until completely set, at least 4 hours and up to 5 days.