Preheat the oven to 325 degrees F (165 degrees C).
Combine 1 cup sugar and water in a saucepan over medium heat. Heat until sugar is dissolved and mixture is thickened and light brown, 7 to 10 minutes. Line the inside of a flan mold with the caramel mixture, tilting the mold to make sure the whole surface is covered.
Combine remaining 1 cup sugar, evaporated milk, egg yolks, and lime zest in a bowl. Gently mix, not beat, until yolks are all broken and blended. Strain the custard through a sieve to remove the zest. Pour mixture into the flan mold. Place flan mold in a larger baking pan filled with water.
Bake in the preheated oven until firm, about 2 hours.