Bring a pot of salted water to a boil. Cook asparagus until tender, about 3 minutes depending on thickness. Drain asparagus and shock it in ice water to stop the cooking; pat dry and set aside.
In a large bowl, whisk together the olive oil, 1 1/2 tablespoons lemon juice and 1/2 teaspoon lemon zest; season with salt and pepper. Add arugula and asparagus spears to bowl and toss gently to coat, being careful not to break asparagus.
On a large cutting board or work surface, arrange 3 slices prosciutto vertically and slightly overlapping to form a rectangle, about 6 by 8 inches.
Lay an even combination of about a 1/4 of the dressed asparagus and arugula horizontally across prosciutto. Tightly roll up prosciutto, jelly-roll style; cut roll on the diagonal into bite-size pieces. Repeat this process to make and cut 4 more rolls.