The fact that MC only managed to find the lyrics for the OP's Beatles 1 Album, given the 27 tracks are the Beatles Singles that made it to the #1 spot in the UK charts, is a bit odd but there is probably a very simple explanation for it - wrongly formatted track names an/or artist names.
This is a list of the Correct Track Names for the tracks on the Beatles 1 Album and MC should always find the Lyrics as they are all on one of the sites it searches:-
Love Me Do
From Me to You
She Loves You
I Want to Hold Your Hand
Can't Buy Me Love
A Hard Day's Night
I Feel Fine
Eight Days a Week
Ticket to Ride
Help!
Yesterday
Day Tripper
We Can Work It Out
Paperback Writer
Yellow Submarine
Eleanor Rigby
Penny Lane
All You Need Is Love
Hello, Goodbye
Lady Madonna
Hey Jude
Get Back
The Ballad of John and Yoko
Something
Come Together
Let It Be
The Long and Winding Road
These 4 wrongly formatted Track Names will always fail to find a match:-
Get Back (Single Version)
Get Back (Single Version) (ft. Billy Preston}
Something (2001 Remaster)
Let It Be (Single Version)
But these 3 correctly formatted alternative Track Names will usually find a match:-
Get Back [Single Version]
Something [2001 Remaster]
Let It Be [Single Version]
This one may also find a match:- Get Back [Single Version ft. Billy Preston] even though putting a featured artists name inside the track name is non-standard.
Most Lyrics Lookup Sites are set up to ignore anything in the track name that is inside square brackets i.e. if fed Get Back [Single Version] it will only use Get Back as the track name and the search will have a better chance of success.
But it will never find a match for any track that has incorrectly formatted track names i.e. Get Back (Single Version) or Something (2001 Remaster).
Incidentally any double or single quotes that are not the straight ones " or ' in a track name will also fail to find a match.
For the benefit of those wondering what the Last Lyrics Lookup field records it simply stores the date on which MC, when triggered Automatically or Manually, carried out a search for the Lyrics for a given track regardless of whether or not it found the lyrics.
There is a limit to the number of tracks that MC can do a "bulk search for lyrics" on, it used to be 12 but I think it has since been reduced to a maximum of 6 tracks.
Mainly down to the simple fact that some Lyrics Lookup Sites allow unlimited access to Humans but restrict the number of times a "search bot" can access the site in a given, usually short, time frame. In addition some sites, and it's not just Lyrics Lookup Sites, can and do limit the amount of metadata a "search bot" can extract.
Incidentally there is another reason why a lyrics lookup may fail that is often overlooked, lyrics lookup sites can only provide those lyrics they are licensed for and there are tracks for which the publisher, usually the Record Company, have never granted a licence to reproduce them.
@M!ke - To get MC to search for and display the lyrics for the track you are playing the CoverArt + Lyrics option should remain selected and never toggled - if MC finds the lyrics it will switch from displaying only the CoverArt to displaying the CoverArt + Lyrics, so if it fails to switch that is proof that MC failed to find the lyrics on any of the sites it searches; either because they are not present or there is something wrong with either the track Name or the Artist name. Unfortunately after correcting either of them inside MC you will have to use the Right-Click Library Tools >> Lookup Lyrics... Option to get it to do a new search on that particular track or wait until the next time it gets played in MC.
@markf2748 - when choosing lyrics by a different artist I hope you are checking to see that both tracks have the same composer and/or lyricist because it's not unusual to find that several artists have recorded tracks with the same track Name but were not written by the same composer and/or lyricist. Something a lot of the well meaning contributors to lyrics lookup website often fail to do.