The US rock band's frontman Wayne Coyne used Twitter and Instagram to reveal the collaboration.
He tweeted: "Miley in the studio vomiting diamonds while singing Lucy In The Sky With Diamonds!!" and posted a photo of the Wrecking Ball singer with embellished diamonds coming out of her mouth.
He also tweeted a photo appearing to show Cyrus rolling a joint while in the studio.
Coyne wrote: "Yup...... Recordin with Miley... High as ****.... #flaminglips #theflaminglips #tulsa #lovemoneyparty."
Lucy In The Sky With Diamonds was written by John Lennon and Sir Paul McCartney and featured on the Beatles' 1967 album Sgt Pepper's Lonely Hearts Club Band.
Wayne Coyne at a concert in February In a 2004 interview Sir Paul confirmed the song is about taking the drug LSD.
It is not the first time the Cyrus and Coyne have worked together.
Last month Coyne and his bandmate Steven Drozd joined the 21-year-old on stage during her Bangerz concert at the Staples Center in Los Angeles.
The Flaming Lips formed in 1983 and are known for their psychedelic rock arrangements.
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