The auction is at Rolling Stone Wyman's restaurant
The wooden stage, from St Peter's Church Hall, in Woolton, Liverpool is expected to fetch up to £50,000.
Also on sale will be the Bechstein grand piano played on most of the White Album and on the single Hey Jude.
The piano can be heard featured on All Things Must Pass, by George Harrison - whose first guitar is among the most important lots at the auction.
Rock star Mick Fleetwood - who co-owns auctioneers Fleetwood Owen - is due to attend the sale, which will be held at Sticky Fingers, the west London restaurant of former Rolling Stone's bassist Bill Wyman.
Other fixtures up for grabs from the unassuming hall include a green hardwood door, a light fitting that hung above the entrance and an exit sign, which is valued at £600.
Auctioneer Ted Owen said: "This exit sign is not just an exit sign - for fans, it has soaked up history.
"When the Cavern Club, where the Beatles famously played, was pulled down, the bricks were going for around £70," he added.
Lennon was playing at St Peter's Hall with his skiffle group, the Quarrymen, on 6 November 1957, when he was introduced to McCartney.
The Quarrymen provided two sessions of entertainment at the Woolton Parish Garden Fête during the late afternoon.
Pianos
The Bechstein grand was used on albums by many other artists, including Elton John, David Bowie, Queen and Supertramp, and on Mary Hopkins's hit Those Were the Days.
The other piano in the sale, a Baldwin satin ebony grand, was given by John Lennon and his second wife, Yoko Ono, to Sam Green.
Mr Green was a close friend of both John and Yoko and assisted them in the purchase of art for their private collection.
He was also an executor of Lennon's will.
After Lennon gave the piano to Mr Green he regularly played it when visiting his home.
The piano is currently on display in the lobby of a bank in Alabama. It is expected to fetch up to £350,000.
Auctioneers said they expected George Harrison's first guitar to sell for between £30,000 and £50,000.
Other lots of interest include a fragment of lyrics and notes in John Lennon's handwriting, posters, rare Super 8 film footage and assorted photographs.