In large pot of boiling, salted water, cook bow ties per package directions.
In a food processor, combine artichoke hearts, lemon juice, Parmesan, and walnuts, and process for 30 seconds. Slowly drizzle in olive oil until mixture becomes a thick paste. Transfer pesto to a large bowl. Season, to taste, with salt and pepper.
Drain pasta and add to pesto in bowl. Toss to coat. Serve hot with grated Parmesan.