“We’re thrilled to be back touring”, yells Lucius’s Jess Wolfe, with a delicious sense of irony. Their new album, Good Grief, is based on the more stressful side of life on the road – not breaking down on the M6 and waiting two hours for the recovery services, but the mental anguish. There are songs about fits of tears and problems on the bus. “My fists are clenched and I’m so angry with you,” the two frontwomen purr in Go Insane.

And yet, here they are, beaming from ear to ear and styled like identical twins. With their red piled hair, heavy eye makeup and strange costumes, they could have stepped from the set of Nic Roeg’s Bowie film, The Man Who Fell to Earth, although those matching capes could also double as Auntie Ada’s curtains.

Their music similarly mixes ancient and modern, plastic pop and soul. With Wolfe and Holly Laessig’s piercing voices way up in the mix, it’s 60s girl group meets synthetic 80s chart hits and the occasional indie rock guitar.

They’re meatier and beatier live than on record, with percussive workouts. Sometimes, they’re that bit too processed, and need some space to breathe, so the homegrown country of Dusty Trails – which finds them huddled around an acoustic guitar, revealing their inner Dolly Partons – comes as a revelation.

A 90-minute set risks outstaying its welcome without any recognised hit singles, and there are lulls, but there’s an unexpected treat when the girls suddenly pop up singing in the audience. Catchiest song Born Again Teen is pure pop bubblegum. By the time they hit peak harmonies with 2013’s Wildewoman, they’re being cheered to the rafters. At this rate, their next album could be all about how touring is wonderful, after all.

• At the Art School, Glasgow, 8 April. Box office: 0141-353 4530. Then touring until 13 April and at Latitude, 13 July.