Combine water, butter, and salt in a saucepan; bring to a boil. Remove from heat; stir in flour until well mixed. Return saucepan to medium heat; cook and stir until dough starts to pull away from the sides of the saucepan, 3 to 5 minutes.
Remove saucepan from heat and stir anise-flavored liqueur, sugar, grappa, and lemon zest into dough. Cool dough to room temperature, at least 30 minutes.
Beat egg yolks into the cooled dough until well mixed. Cover bowl with a clean towel and let rest for 3 hours.
Beat egg whites in a bowl until stiff peaks form; gently fold into the dough until no white streaks remain.
Heat lard in a heavy saucepan over medium heat or in a deep fryer. Form dough into balls the size of golf balls; fry in the hot lard in batches, until doughnuts are lightly browned and cooked through, 4 to 5 minutes.