Preheat the oven to 350°F.
Add the sugar to a medium-sized sauce pot, and place it over medium-high heat. Watch it carefully and do not stir. Once the sugar begins to melt and becomes an amber color, swirl the pot every so often, gently until the sugar has completely dissolved. This will take about 5 to 10 minutes, and it will be a medium amber color at this point. Immediately pour in a 9 x 2-inch cake pan (or pie dish, or special flan pan) and quickly swirl it around to coat the bottom. The goal is to cover the entire bottom, but don’t worry if it doesn’t quite make its way to the edges, as it will melt again in the oven.
Add the milk, sweetened condensed milk, eggs, lemon zest, lemon juice and vanilla to a blender. Blend until it’s smooth, about 5 seconds. (You can also use an electric mixer and a mixing bowl to do this.)
Place the prepared pan in a large roasting or baking pan. Pour the egg mixture into the cake pan, over the caramel coating. Add enough hot water to the roasting/baking pan, to come halfway up sides of the cake pan. (This is called a water bath, and adds moisture to the oven, which keeps the flan from becoming rubbery or cracking.)
Loosely cover the cake pan with foil, and bake flan in the preheated 350°F oven in the water bath until it no longer jiggles, 50 to 60 minutes. Carefully remove the cake pan from the water bath and place it on a cooling rack. Let it cool there for about 90 minutes. Then place it in the refrigerator for at least 3 hours, and ideally overnight.
Run a knife along the edges of the pan to loosen it. Place a flat platter, that’s larger than the cake pan upside down on top. Then holding the two together, invert the flan onto the platter.
Add lemon slices if desired and serve!