Drain the asparagus, dry with paper towels, and slice into ¼-inch pieces. Set aside.

Combine the cheeses, lemon juice and zest, chives, salt, and pepper, mixing until fully combined.

Divide the mixture equally among the wraps and spread into an even layer, covering the entire wrap.

Sprinkle on the sliced asparagus and chopped peppers. Roll tightly, then wrap each roll individually in plastic wrap. Refrigerate for at least 2 hours or up to 1 day.

Before serving, slice into ¼-inch slices and serve on a platter.