Combine sugar and lemon juice in a medium saucepan; bring to a simmer over medium heat, stirring occasionally.
Whisk egg yolks in a medium bowl. Gradually pour hot lemon mixture into the bowl, whisking constantly until combined. Return mixture to saucepan. Cook over medium, stirring and scraping bottom of pan constantly with a rubber spatula, until mixture simmers. Continue to simmer gently until thickened, 3 to 5 minutes.
Remove from heat and stir in vanilla extract. Whisk in butter until melted, or use an immersion blender to blend until smooth. Pour through a strainer into a clean bowl. Cover and refrigerate at least 8 hours and up to 1 week.