Combine sour cream, lemon juice, mustard, ½ teaspoon salt, and ¼ teaspoon pepper in bowl; set aside sauce.
Place ¼ cup flour in shallow dish. Beat eggs in second shallow dish. Process bread, 1 teaspoon salt, ½ teaspoon pepper, and remaining 3 tablespoons flour in food processor until finely ground, about 1 minute. Transfer bread-crumb mixture to 13 by 9-inch baking dish.
Place asparagus in colander and rinse under cold running water. Shake colander to lightly drain asparagus (asparagus should still be wet). Transfer one-third of asparagus to flour and toss to lightly coat; dip in egg, allowing excess to drip off; then transfer to bread-crumb mixture and press lightly to adhere. Transfer breaded asparagus to baking sheet. Repeat with remaining asparagus in 2 batches.
Line large plate with paper towels. Heat oil in large Dutch oven over medium-high heat to 350 degrees. Carefully add one-third of asparagus to hot oil and cook until golden brown, 1 to 2 minutes. Transfer to prepared plate. Repeat with remaining asparagus in 2 batches. Serve with sauce.
