Heat oven to 350°F. Place a rack in the lower-middle position.
Fit the pie crust into a 9-inch pie plate. Crimp edges and chill while you mix the filling.
Whisk sugar, flour, cornmeal, salt, and nutmeg in a large bowl until no lumps remain.
Add eggs one at a time, whisking until silky and thickened slightly.
Stream in the melted butter while whisking. Stir in buttermilk, vanilla, lemon juice, and zest until smooth.
Pour filling into the chilled crust. Lightly tap the pan to release air bubbles.
Bake 25 minutes, then tent crust edges with foil. Continue baking 20–25 minutes until the center has a slight wobble.
Cool on a rack until room temperature, then chill 1 hour before slicing for the cleanest cuts.