Not sure if this is a bug or a feature of engraving options not setup right? I searched it up and seems like it should work (Moving lyric lines vertically)
These lyrics are actually drum stickings. I am not able to adjust them vertically in any of the parts or score. They look mostly correct in the score, it is just this drumset part that has an issue (too far from staff, likely displaced by my bar numbers here)
Assuming you are in Engrave mode, when you click on the leftmost lyric a small edit handle should appear there. Click on that and then use alt + up/down arrows to move the whole line of lyrics vertically.
You see the box only when you select the first syllable, but selecting and moving any syllable on the line has the same effect of moving them all together. At least it does for me! @emusic if you still can’t move them, post a project that demonstrates this and we’ll have a closer look.