Preheat oven to 350℉. Grease loaf pan with butter then dust with flour to coat bottom and sides of the pan. Dump out any excess flour. 

Process sugar, eggs, vanilla, lemon zest, and lemon juice together in a food processor until combined, about 10 seconds. 

With the food processor running, add hot melted butter in a steady stream until incorporated. 

Pour mixture into a large bowl. 

Sift flour into the egg mixture, in three additions. Whisk to combine flour and egg mixture after each addition, until just a few streaks of flour remain. Whisk the batter gently until almost no lumps remain. 

Pour batter into the prepared pan, smooth the top of the batter, and gently tap the pan on the counter to settle the batter.  

Bake the cake for about 50 minutes ( if 8 ½ by 4 ½ inch loaf pan) or 45 minutes (if 9 by 5 inch loaf pan), rotating pan halfway through baking. The cake is done when the toothpick comes out clean after being inserted in the center.

 Let cake cool in the pan for 10 minutes. After removing from pan, let it cool completely.