Preheat oven to 350°F (175°C). Grease a 9-inch pie pan.

In a large mixing bowl, combine sugar, flour, and salt. Whisk until mixed.

Add eggs to dry ingredients and beat until combined.

Gradually mix in milk and melted butter, stirring until smooth.

Stir in lemon zest, lemon juice, and vanilla extract until fully incorporated.

Pour batter into the prepared pie pan.

Bake in preheated oven for 40-45 minutes, or until the top is golden and a toothpick inserted in the center comes out clean.

Allow pie to cool at room temperature for at least 30 minutes before slicing.