Heat 1-inch vegetable oil in a deep-sided skillet over medium heat.

Whisk buttermilk, lemon zest, paprika, and black pepper together in a wide bowl. Pour flour into a separate wide bowl. Place a paper towel-lined plate near the stovetop.

Dip 1/3 of asparagus into buttermilk mixture. Dredge in flour; coat thoroughly. Repeat with a second layer of buttermilk mixture and flour. Place coated asparagus, unstacked, onto a baking sheet. Repeat with remaining asparagus.

Fry coated asparagus, in three batches, in hot oil until golden brown, 2 to 4 minutes. Transfer to the paper towel-lined plate. Repeat frying until all the sticks are cooked. Serve immediately.