Preheat oven to 400 degrees F (200 degrees C). Lightly grease a baking sheet.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes.
Drain the bacon slices on paper towels. Crumble bacon when cooled.
Cook asparagus in a skillet with a small amount of water over medium heat until crisp and tender, about 6 to 8 minutes; drain and sprinkle with lemon juice.
Flatten bread slices with a rolling pin.
Stir cream cheese, crumbled bacon, and chives together in a small bowl until evenly mixed.
Spread 1 tablespoon of the cream cheese mixture onto each slice of bread and top with an asparagus spear.
Roll the bread tightly around the asparagus; arrange onto prepared baking sheet with seam side down.
Brush the tops of the rolls with melted butter and sprinkle with Parmesan cheese.
Bake in preheated oven until lightly browned, 10 to 12 minutes.
