NEW YORK—Lululemon Athletica Inc. on Monday followed through on its threat to sue Peloton Interactive Inc. over the “copycat products” in the exercise bike company’s new clothing line. The Canadian athletic apparel maker sued Peloton in Los Angeles federal court, seeking triple damages for its rival’s alleged “willful” infringement of six design patents. Lululemon filed its lawsuit five days after Peloton brought its own case in Manhattan federal court, seeking a declaration that Lululemon’s claims had no merit. Peloton and its lawyer did not immediately respond to requests for comment. The dispute arose from Peloton’s launch in September of a private-label apparel brand, following the end of the companies’ five-year co-branding relationship. Lululemon said five Peloton women’s bra and legging products—Strappy Bra, High Neck Bra, Cadent Peak Bra, Cadent Laser Dot Bra, and Cadent Laser Dot Leggings—infringed its patents. It also said another Peloton product, One Lux Tight, is a knockoff of …