In a medium saucepan, combine the water, butter and sugar. Bring to a boil, then turn off the heat and stir in the flour. Stir until the mixture forms a ball. Move the batter to a medium bowl and let cool.
Use an electric mixer to beat in the eggs, one at a time. Add lemon extract and a pinch of salt.
Fill a medium pot with about 3 inches of canola or vegetable oil and heat over medium-high heat until it reaches a temperature of 375 degrees. See Recipe Notes below if you don't have a thermometer to check the temperature.
Drop the doughnut batter into the hot oil by teaspoon (no bigger than an actual teaspoon because they will puff up a lot while cooking). You can fry about 15 doughnuts at a time. Fry until they are lightly browned all around. Remove with a slotted spoon onto paper towels to drain.
Roll in sugar while the doughnuts are still warm, and serve immediately.
If you don't have a thermometer for checking the temperature of the oil: Use the handle of a wooden spoon. When the oil has preheated, dip the handle of a wooden spoon into the oil. If the oil starts steadily bubbling, then the oil is hot enough for frying. If the oil bubbles very very vigorously, then the oil is too hot and needs to cool off a touch.