The 39-year-old singer and the 28-year-old pop star have teamed up for a version of classic song 'Dream a Little Dream of Me', which has been recorded over 60 times by artists such as Ella Fitzgerald, The Mamas & The Papas, Doris Day and Dean Martin.
Although Lily was thrilled when Robbie asked her to join him on the track she confesses she was a bit nervous when she got in the studio with him.
She said: '''Dream A Little Dream' is one of my favourite songs of all time so I didn't hesitate when Robbie asked me if I'd like to duet with him on it. I was a bit nervous when we recorded it, especially when I asked him what he wanted me to do and he said something like 'just be you'. But I'm really happy with it and think we do justice to a classic song.''
Robbie and Michael sing together on 'Soda Pop' and the Canadian crooner believes fans will enjoy the fun track.
Michael said: ''The song is for his new album and it's so good. We had too much fun making it.''
As well as a number of swing classics, the LP - which will be released on November 18 - also contains six original songs with Robbie co-wrote with songwriting genius Guy Chambers.
It is Robbie's first big band album since 2001's 'Swing When You're Winning'.
'Swings Both Ways' full tracklisting:
'Shine My Shoes'
'I Wanna Be Like You' - featuring Olly Murs
'Swings Both Ways' - featuring Rufus Wainwright
'Dream A Little Dream of Me' - featuring Lily Allen
'Soda Pop' - featuring Michael Buble
'Puttin' On The Ritz'
'Little Green Apples' - featuring Kelly Clarkson
'Minnie The Moocher'
'If I Only Had A Brain'
'No One Likes A Fat Pop Star'
The actress thinks it would be tough to recast her character, Winifred Sanderson.
Beck wishes he'd had ''more fun'' when Kanye West invaded the stage in protest at his 2015 Grammy Awards win.
The Duffer Brothers wanted to "experiment a little bit".