In a medium saucepan, combine the water, butter, sugar, and salt. Bring to a rolling boil over medium-high heat, stirring until the butter is fully melted.
Remove the saucepan from the heat. Add the gluten free flour and tapioca starch all at once and stir vigorously with a wooden spoon until the mixture forms a smooth ball of dough that pulls away from the sides of the pan.Return the pan to medium-low heat and continue stirring for about 1 minute to cook the dough slightly and dry it out a bit.
Transfer the dough to a large bowl and let it cool for 5 minutes. Add the eggs one at a time, beating well with a wooden spoon or hand mixer after each addition. The dough will look slippery at first but will come together into a smooth, thick, pipeable batter.Stir in the vanilla and lemon zest.
Fill a heavy-bottomed pot or Dutch oven with about 3 inches of vegetable oil and heat to 350 degrees F. Line a plate or baking sheet with paper towels.
Using two spoons or a small cookie scoop, carefully drop rounded tablespoons of dough into the hot oil, working in batches of 4 to 5 so you don't crowd the pot. Fry for 3 to 4 minutes, turning them occasionally, until they are puffed, deeply golden brown on all sides, and cooked through in the center.Transfer to the paper towel-lined plate.
While the zeppole are still warm, dust them generously with powdered sugar. Pile them on a serving platter and serve immediately while they are hot, puffy, and irresistible.