ODDBALL: And yet Safe Inside the Day is an accessible showcase.

She goes by the name Baby Dee, even though she was born in Cleveland in 1953. And her résumé reads like something out of the Katherine Dunn novel Geek Love: a decade as the organist and music director at a Catholic church in the Bronx, then on to the Coney Island circus, where she played accordion and was billed as the “Bilateral Hermaphrodite” (in part because she is a transgendered woman). And, having received classical training as a harpist, she went on to tour Europe and North America with the Bindlestiff Family Circus. Oh, and when she wasn’t on the road, she performed on the streets of Greenwich Village with her harp and a tall tricycle. In short, she’s spent the past several decades becoming a legend in the performance-art underground. Now she’s signed a deal with hip Chicago indie Drag City to release her new album, Safe Inside the Day.

It’s not her first album: from 2000 through 2005 she recorded several discs for a tiny label run by British musician David Tibet, Durtro Records. But Safe Inside the Day will likely bring the first real exposure to an American audience for the flamboyant Dee, who supports the disc with a show at the Lily Pad this Sunday. The album finds her working with an intriguing collection of indie-rock luminaries: Bonnie “Prince” Billy (a/k/a Will Oldham), Matt Sweeney (of Zwan and Superwolf), Andrew W.K. But Dee is very much her own show — and an accessible one at that. On the new disc, she delivers cabaret torch songs with a touch of vaudeville playfulness anchored by heavy percussive piano runs, as well as straightforward instrumentals (“A Christmas Jig for a Three-Legged Cat” and “Flowers on the Tracks”) that, pretty and accomplished, wouldn’t be out of place in the hands of — honest — Billy Joel. There are hints of Kurt Weill in the theatrical flair of “The Only Bones That Show.”

And then there’s the influence of those years in the circus. “My music back then,” she tells me over the phone, “was a bit opaque — a little brassy. I like to think I’ve gotten away from that, but I still go there once in a while. I always think of Felix the Cat and his bag of holes. Take out a hole and jump in. There’s an element of that in it for me.”

She also explains how her life and music have been molded by the outrageous characters she’s met and worked with along the way. “The things I’ve loved most in my life have been made by anonymous oddballs. I worked for a wonderful show in Islington, London, called ‘The Voluptuous Oddball Circus Sideshow.’ It was run by Otter. Otter taught me how to dance naked on a bar. She was the best pole dancer that ever lived, and she could blow a 20-foot ball of fire out of her vagina. I don’t think it’s possible to know great people like that and not be influenced by them.”

But even though Dee somehow brings the Catholic saints who were once her inspiration together with oddballs like Otter, Safe Inside the Day doesn’t strain to be strange or difficult. “I’m not a crusader for freakdom or anything like that. I’ve never been a rebel, believe it or not. It’s too reactionary, not my style. There were a few years in the ’90s where I may have made myself a little scary, but I like to think I’ve grown out of that.”

BABY DEE + THE PRANA TRIO | Lily Pad, 1353 Cambridge Street, Cambridge | February 3 | 617.395.1393