Using a peeler, remove the zest from the lemons, avoiding the white pith. In a medium bowl, combine the lemon zest and the sugar, stirring with a wooden spoon until the sugar is fragrant and has the texture of soft, fresh snow, about 10 minutes. Add 3/4 cup boiling water to the bowl and stir to dissolve the sugar. Strain the syrup and let cool.
Juice the lemons and strain the juice —you’ll need 1 cup plus 2 Tbs. juice.
At least 3 hours and up to 6 hours before serving, combine the syrup, lemon juice, wine, aquavit, strawberries, and cucumbers in a large bowl or pot. Chill in the refrigerator.
Just before serving, pour the punch into a large chilled punch bowl or dispenser, with a block of ice. Add the sparkling water and gently stir.