You're right somehow, but it was probably Shaved Fish, released on CD in May 1987, that they didn't want to repeat (with Imagine as the only track on both releases).
The John Lennon Collection came out some years before this - around 1982. I suppose the track selection here was an attempt to avoid too much duplication, but three songs from Double Fantasy seems a bit much.
Yes, it does have Real Love (Acoustic Guitar Demo Take 6 of 7), which is a bore as far as I remember, and Imagine (Rehearsal) where Lennon breaks off midway through the recording. Both tracks are for completists though, nothing that I actually miss.
Yet another one to be made International, as my Made in UK copy was purchased in Australia. I notice that the (C) credit on the disc is EMI Records Ltd., and not Capitol Records inc. as shown on the back. There is also a UK catalogue number, CDPCSP 722, on the back and disc, so I'll insert that in a minute. And Syd, it looks like you didn't notice that the back shows asterisks next to tracks 2-10, and immediately under track 7 is the notation "*PERFORMED BY THE BEATLES".
It does have a couple of tracks that I don't think have appeared anywhere else since (officially):
"Real Love" (Acoustic Guitar Demo Take 6 of 7) and "Imagine (Rehearsal)".
This was one of my early CDs. Although the Beatles tracks here are great and belong to Lennon's most personal songs, I found it an erratic compilation, with various incomprehensible omissions of his solo work. Anyway I had to buy it because it was the first album which included the unabridged single version of Give Peace A Chance.
When I noticed this entry here, I initially thought I'd still own the CD but obviously I replaced it with the slightly more representative John Lennon Collection that came out one year later.