Leisz grew up in the garage band culture of mid-1960s Southern California. He spent time at the Ashgrove, the Troubador, and clubs on the Sunset Strip . He began playing guitar and soon added dobro and lap steel. He was inspired to pick up the pedal steel after hearing Sneaky Pete Kleinow and Buddy Emmons. In 1975, he toured with John Stewart (formerly of The Kingston Trio). He was a member of Funky Kings who released their eponymous debut album on Arista Records in 1976. After the band broke up, he became a popular musician both in the studio and on the road.
In 1987, Leisz began working with Dave Alvin (formerly of The Blasters). Their collaboration led to Leisz producing several of Alvin's albums, including King of California, Black Jack David, Ashgrove, and West of the West. In 1989, he played on k.d. lang's Grammy-winning Absolute Torch and Twang and joined her on the resulting tour. For the next eighteen years he toured with Lang and recorded with her, including her album Ingenue. Starting the early 1990s, he worked often with Matthew Sweet, played on Sweet's album Girlfriend and toured with him.
In January 2008, Leisz joined the group Works Progress Administration, a band composed of Leisz, Sean Watkins (guitar), his sister Sara Watkins (fiddle), Glen Phillips (guitar, vocals), Benmont Tench (piano), Luke Bulla (fiddle), Pete Thomas (drums), and Davey Faragher (bass). The group released their debut album, WPA, on September 15, 2009.
In 2010 and 2011, Leisz toured with Ray LaMontagne as a member of his backing band, The Pariah Dogs. He toured in 2013 as a member of Eric Clapton's band, in 2015 as a member of Jackson Browne's band, and again in 2017. He appeared in the 2016 Cameron Crowe cable television series Roadies, accompanying Jackson Browne on three songs in the last episode of the series.
Leisz's playing has appeared throughout the years on recordings by Aaron Neville, Alison Krauss, Amos Lee, Beck, Bill Frisell, Black Crowes, Bon Iver, Bruce Cockburn, Bruce Springsteen, Cass McCombs, Chuck Prophet, Daft Punk, Dave Alvin, Eagles, Emmylou Harris, Eric Clapton, Glenn Frey, Grant Lee Buffalo, Haim, Jackson Browne, Joe Cocker, John Fogerty, John Mayer, John Stewart, Joni Mitchell, k.d. lang, Lucinda Williams, Matthew Sweet, Meshell Ndegeocello, Paula Cole, Peter Case, Ray Lamontagne, Robert Plant, Sam Phillips, Sara Watkins, Shawn Colvin, Sheryl Crow, Susanna Hoffs, The Bangles, The Jayhawks, The Smashing Pumpkins, Tracy Chapman, Whiskeytown, Wilco, and Allen Toussaint.
Another close collaborator is Bill Frisell, with whom he tours regularly and is featured on the albums Good Dog, Happy Man, Blues Dream, The Intercontinentals, Disfarmer, All We Are Saying, and Guitar in the Space Age!