Ono mentioned the songs at a meeting with the show's creative team last month.
"My head was about to explode," Scardino said.
Two of the songs, which were on a homemade recording of Lennon's, had never even been published.
"India, India" is about Lennon's trip to India and "I Don't Want to Lose You" is a ballad that will be used at a point in the show when Lennon and Ono reunite after a separation.
The third song, "Cooking in the Kitchen of Love," was recorded by Ringo Starr but never by Lennon.