from the very long wikipedia account of LCL

"The lawn chair used in the flight was reportedly given to an admiring boy named Jerry, though Walters regretted doing so when the Smithsonian Institution asked him to donate it to its museum.[12] Twenty years later, Jerry sent an email to Mark Barry, a pilot who had documented Walters's story and dedicated a website to it, and identified himself.[13] The chair was still sitting in his garage, attached to some of the original tethers and water jugs used as ballast.[12] The chair was placed on loan to the San Diego Air and Space Museum, where it was exhibited in 2014.[14] It was later donated to the Smithsonian and is on display at the Steven F. Udvar-Hazy Center in Virginia."