Called Making It New, the five-minute song will receive its world premiere in April when the Renfrew Street building is officially opened. It will be performed by the GSA Choir, to music by Glasgow-born composer Ken Johnston.
"It's about art and creativity," Lochhead explained. "It's about how art comes from a small seed and it's about working on art. It's about technique and about learning technique, and about how you should be able to actually produce the art.
"I suppose it's probably an anti-conceptual art song. One of my favourite bits of the lyrics is: 'It takes technique to achieve what is to our species unique - art.'" The Reid Building - named after the GSA's former director Professor Seona Reid - is currently being completed opposite the Mackintosh building in Glasgow's city centre.
Its interior is taking shape and just last week the caps were removed from the tops of three "driven voids of light" which allow natural light to flood into the depth of the building.
The project for a new choral work, which received Creative Scotland funding, is the brainchild of 22-year-old GSA student Jamie Sansbury who, as well as studying architecture at the school, is also its budding Gareth Malone: a veteran of the National Youth Choir of Scotland in his native Edinburgh. He set up the GSA Choir in 2012 and, from humble beginnings, it can now draw on the voices of up to 50 singers.
"It's a three-part piece, but you could have it sung by 100 people or 20," he explained.
"I'm expecting there to be 55 people when we start rehearsals, but because of the prestige of this commission I would imagine we might get five or 10 other folk added to that."
It was Mr Sansbury who asked GSA graduate Lochhead to take part in the project and who nudged her in the direction of musical theatre and the great American composers of the mid 20th century. It turned out it was a subject she knew well already.
"My inspiration was the songs of certain musicals that I love," she said, "particularly those Jewish songwriters of the 1940s and 1950s like George and Ira Gershwin, Stephen Sondheim, Lorenz Hart, those sort of people who were playful with lyrics.
"I like reading their lyrics - one of my favourite books is the entire lyrics of Ira Gershwin, which has lots of comments from him. He's not just one of my favourite lyricists of the 20th century, he's one of my favourite poets too."
Her lyrics make mention of Charles Rennie Mackintosh, who designed the famous landmark the new building faces, but the idea is for the core of the song to be able to be used on other occasions and to have a life beyond next April's investiture.
"We were all quite determined the piece could have a life outside the premiere," said Mr Sansbury. "So obviously the song needs to celebrate the building in some way - that's why we're singing in it - but we were quite keen to celebrate what goes on inside the building and the creativity that goes on at the art school so that other folk might want to sing it in the future. So it's become a piece about creativity and art, bookended by a verse about the new building and another with a brief mention of the Mackintosh building."
As yet, Lochhead has not heard her words sung by the choir - rehearsals don't start until next month - and she is not expecting a phone call from Andrew Lloyd Webber when she does.
That, though, is not her biggest regret. "I love choirs," she said. "I wish I could sing well enough to join one - but I was always told to do silent singing at primary school."