Boil the kettle. Sift the gluten free flour into a big mixing bowl with a big pinch of salt, baking powder, then stir in the 2 tbsp sugar and lemon zest.
Put 350ml boiling water, the lactose free butter and vanilla extract in a saucepan. Heat gently to melt, then bring to a simmer and, as soon as it is boiling, turn off the heat.
Tip in the gluten free flour mixture and very quickly beat with a wooden spoon until lump-free. Cool for 5 mins, then beat in the eggs one at a time, with the spoon or an electric whisk. Rest for 10-15 mins, or cover and chill for up to 24 hrs.
Fill a large, deep saucepan one-third full of oil. Heat until it reaches 180°C on a cooking thermometer. Cover a tray with kitchen paper, and mix the caster sugar and cinnamon together in a bowl.
Fit a star nozzle to a piping bag – 1-2cm wide is a good size. Fill with the rested dough, then pipe 2-3 strips directly into the pan, snipping off each dough strip with a pair of scissors.
Fry until golden brown and crisp, then remove with a slotted spoon and drain on the kitchen paper-lined tray. Carry on cooking the rest of the dough in batches, sprinkling the cooked churros with some cinnamon sugar as you go.