The 'Hard Out Here' singer has joined Miley on the latest leg of her 'Bangerz' US tour and after catching the show in London in May, Lily was blown away by Miley.
She told Billboard: ''I saw it at The O2 in London, and I'm not exaggerating when I say it's one of the best shows that I've seen in years. It's up there with an Oasis show or The Stone Roses or something. It's kind of incredible to watch - she's a real force. There's no two ways about it, she's meant to be up there doing that.
''She's incredible, and she has such a presence. Her personality is what shines through. I'm not close to Miley. I don't know her very well, but I feel proud of her.''
Lily is a big fan of Miley and recently revealed plans to introduce daughters Ethel, two, and 18-month-old Marnie, to the 'Wrecking Ball' singer when her kids join her in the States.
Lily - who is married to Sam Cooper - said: ''They are going to meet me in New York and then come on the bus with me and Miley.
''Although I don't think Miley will be on my bus, she's probably got other plans!''
The guitarist came up with the band name in 1982.