I am even more puzzled now. I just checked, and my iPod Touch does in fact run 11.2.5 like yours. Having two different iPods running the same software version with two different outcomes seems to be the case.
"Random tapping" might not have been the right expression, but the point is, that finding the lyrics now, after the software update, is different than before.
When I tap (hold it for a few seconds) on the song title, I get a pop up window with the album/song picture on the upper left, with the song title, artist name and album name to the right of the picture. Then the list below gives me 7 choices (my list is in Danish, but I've translated it, and I've added the Danish text in parenthesis, so you can see which menu option is what in the pictures below):
(Fjern) "Remove..." with a trash can icon on the right
(Føj til en spilleliste...) "Add to playlist"... with a symbol with a plus and four lines
(Aspil som næste) "Play as next" with a symbyl showing four lines and an arrow pointing to the line on top
(Aspil senere) "Play later" with a symbol with four lines and an arrow pointing to the line at the bottom
(Del sang...) "Share song..." with a symbol with a box and an arrow pointing skywards
(Tekster) "Lyrics" with a quote symbol and four lines
(Vurder sang) "Rate song..." with a star symbol
Below these choices there are two hearts: One full heart and a full heart with a line across it
At the bottom of this pop up window there's an option to "Cancel".
Showing it instead of telling it is a lot easier, I figure, so I just took a picture of my iPod Touch with my smartphone, then emailed the pictures to myself so I could share the pictures with you here. 🙂


As you can see from the pictures, you have to scroll a bit (like I mentioned previously) in order to see the Lyrics (Tekster) option. The "Lyrics"/"Tekster" option is number 6 in the menu, and when you tap to open this menu, you only see the 4½ first options.
I have no idea why our iPods do not behave the same, when everything tells us that they should. FYI: My iTunes is also updated with the newest software (at least as far as I know). It runs version 12.7.3 in case that makes a difference. The strangest thing is that my iPod Touch shows lyrics and yours does not even though they run the same, updated version of iOS.