The last song he recorded was called "I Don't Wanna Face It."
No. The song "Imagine" was not the last song John Lennon wrote. In fact, he released the song "Imagine" on his 1971 album titled "Imagine" as well. The last song that John Lennon worked on upon the time of his death was his wife Yoko Ono's song "Walking On Thin Ice". The last song that John Lennon actually released himself was "I Don't Wanna Face It," released on wife Yoko Ono's mesh of unreleased Lennon/Ono songs after the time of John's death. John Lennon died on December 8, 1980, and wife Yoko Ono released the last album containing new, original Lennon songs (Milk and Honey) on January 27, 1984.
John Lennon wrote the song.
God - John Lennon song - was created in 1970.
Look at Me - John Lennon song - was created in 1970.
Remember - John Lennon song - was created in 1970.
It was John Lennon.
John Lennon, during 1968.
Love - John Lennon song - was created on 1982-11-15.
FAME
Borrowed Time - John Lennon song - was created on 1984-03-09.
Here We Go Again - John Lennon song - was created in 1986.