Heat water, lemon wedges, and white sugar in a large saucepan over medium heat. Simmer until sugar is dissolved, mashing lemons often to release juice and oils.
Cook and stir lemon mixture for 5 minutes more, then remove from heat and allow to cool slightly. Strain lemon pieces from saucepan.
Sprinkle gelatin into saucepan.
Heat syrup and gelatin mixture over low heat until gelatin dissolves, 5 to 10 minutes.
Remove from heat and allow to cool for 15 minutes. Pour lemon vodka into gelatin mixture and stir well.
Pour mixture into a 9x13-inch baking pan; refrigerate until set, at least 6 hours.
Run a sharp knife under hot water; cut gelatin into cubes with knife and sprinkle cubes with turbinado sugar before serving.
