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.
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!