The 'When She Was Mine' pop band wrote material with the Take That singer, but the songs were not included on their debut album due to time restraints.
Band member Andy Brown explained that they hope to release a deluxe version of their forthcoming LP that will feature the Barlow tracks.
"Take That are on the same label as us - Polydor - and we also work with the same producer, so Gary heard some of our stuff and really loved it," Brown told the Daily Star.
"We went in and wrote together and it was a dream come true. He's an amazing guy and a great writer so I couldn't have asked for more."
He added: "It was such a fast two days. We had six hours to write a couple of songs but as the album is already finished we'll have to do a deluxe version later to get them out."
One of the tracks was a ballad titled 'Living in My Shadow', which proved to be emotional for the band.
Ryan Fletcher said: "When I went in to record my bass part I was in tears."
Adam Pitts added: "The lyrics are unbelievable. It's a beautiful song."
> Lawson wouldn't audition for X Factor: 'We did the proper band thing'
Lawson performed at the Hard Rock Calling event in Hyde Park at the weekend on the Pepsi Max Stage.
The band's second single 'Taking Over Me' will be released on August 5.
Watch the video for 'Taking Over Me' below: