The show's writer-director, Don Scardino said earlier this week that the songs "India, India," written after the Beatles visit to India in 1968, and "I Don't Want To Lose You," an introspective ballad, will be included in the show.
The songs exist only on private recordings Lennon made toward the end of his life. Ono gave "I Don't Want To Lose You" to the surviving Beatles when they reunited in 1990 for "The Beatles Anthology" but an electronic hum in the recording made it impossible to use.
Ono was quoted as saying she was releasing her husband's unpublished songs whenever she found ways of "presenting them in the right way."
"For these two songs, I thought the musical would be a very effective, beautiful way to do it," she said.
Lennon was shot to death outside his Manhattan apartment building in 1980.