To Lovett’s point, “This Old Porch” can operate without Gilmer, but his gentle, rhythmic push becomes the song’s heartbeat. “We rode a lot of miles together,” Lovett said of Gilmer.

“I’ve been singing about nakedness a lot lately,” Lyle Lovett says by way of introduction to It’s a Naked Party, which he wrote with his seven-year-old twins. As he points out, the older ...