Cream sugar, lemon zest, and softened butter together. Whisk in the eggs and lemon juice. Pour mixture into a saucepan and cook over medium heat, stirring constantly, until a thermometer registers 175 degrees Fahrenheit. Immediately remove from heat and whist in a pinch of salt. Strain into a bowl and allow to cool at room temperature for 15 minutes. Cover with plastic wrap, so that the plastic wrap rests on the curd, and refrigerate until further use, at least two hours.
Preheat oven to 325 degrees Fahrenheit. Grease and line two round bake pans. In the bowl of an electric mixer fitted with a paddle attachment, cream butter and sugar together until light and fluffy, about 5 minutes. Add the eggs, lemon juice, and zest with the mixer on stir and beat until fully combined.
In a separate bowl, sift together flour, salt baking powder, and baking soda. Alternatively mix in the flour mixture and the buttermilk to the egg mixture in the mixer and mix until just combined. Divide the batter amongst the cake pans and bake for 40-50 minutes or until a tester inserted in the cake comes out clean.