For the vinaigrette: Add the vinegar and capers to a small bowl. Whisk in the olive oil and season with salt and pepper.
For the asparagus: Heat the grill to medium-high.
Carefully wrap 2 asparagus at a time with 1 or 2 pieces of lardo, overlapping as you go. (If your lardo is cut paper-thin, then 2 will be easier to work with. If thicker, then one should be sufficient.)
Lay the asparagus cross-wise across the grill to keep it from falling through the grates. Grill, turning occasionally, until just tender and charred and the lardo has rendered and started to become crispy, 8 to 10 minutes. Remove from the grill and set aside. Drizzle with vinaigrette before serving.
NotesCook's Notes: It may look like the lardo is melting off of the asparagus as you cook it...be patient! It will eventually crisp up and stay put. You may want to make extras - because these will go fast!
For advanced preparation, make this vinaigrette in a jar with a lid. Add all of the ingredients and give it a shake!