For the caramel: Set a rack in the middle of the oven and preheat to 350°. Set a kettle of water on to boil. Combine sugar and lemon juice in a small saucepan. Bring to a boil over medium-high heat, stirring with a fork, just until sugar dissolves, about 3 minutes. Stop stirring and let the sugar gradually caramelize until deep golden brown, about 4 minutes more. Remove from heat and carefully divide caramel between eight 3 1⁄4"-wide flan molds or ramekins to form a layer in the bottom of each. Set the molds aside.
For the custard: Put 6 tbsp. of the sugar, milk, vanilla, and zest into a small pot. Bring just to a boil over medium-high heat, then remove from the heat. Discard the lemon zest. Whisk together the remaining sugar and eggs in a large bowl. Slowly pour the milk mixture into the egg mixture, whisking constantly, until well combined.
Arrange the molds in a deep baking dish and pour the milk-egg mixture evenly into them. Put the baking dish into the oven and pour in enough hot water from the kettle that it comes halfway up sides of the molds. Bake until flans are set around the edges but still slightly wiggly in the center when the sides are tapped with a spoon, about 30 minutes. Let flans rest in water bath for 5 minutes, then remove and transfer to the refrigerator to let chill completely.
To serve: Carefully run a sharp knife around edges of each mold. Dip the bottoms of each mold briefly into a bowl of hot water to warm them slightly. Invert the flans onto small plates, knock on the bottoms for good luck, and lift the molds off to reveal the flans.