Mix water and yeast together in a small bowl. Let stand until foamy, about 15 minutes.

Combine flour, eggs, butter, 1/2 cup plus 2 tablespoons sugar, and lemon zest in a large bowl; add yeast mixture. Knead by hand until dough comes together. Cover with a clean dish towel. Let rise in a warm place until doubled, about 2 hours.

Roll out dough into a large rectangle on a lightly floured work surface. Cut into diamond shapes using a small pastry wheel cutter. Brush off excess flour.

Heat oil in a deep saucepan or wok. Cook doughnuts in batches until golden brown, about 1 minute per side. Drain on a paper towel-lined platter.