per redcarpet.united.com

How do I obtain a new United Club membership card?

Visit the join/renew page to renew your United ClubSM membership.

If your United Club membership card has been lost, misplaced or stolen, please phone our Service Center toll-free at 1-866-UA-CLUBS (822-5827) between the hours of 8:00 AM and 8:00 PM CST. A replacement fee of $50 USD will apply. Please note that if you do not have your membership card, you may access any lounge by providing your Mileage Plus number upon entry.

However, if you go to update your membership information, the screen they present you is basically a membership card. Print it.