Montxo:

I did some experimenting on a song with bar-based lyrics.
To delete the intro bars, and move the chords and lyrics from bar 9 to bar 1,
I simply hightlighted the 1st 8 bars in the chord grid, and used Edit > Delete Bars.

That removed the 8 bar intro (with no lyrics) and moved bar 9 to the beginning, along with the lyrics for bar 9 and all the bars following.

In general, if you want to move bar-based lyrics, highlight the bars containing the lyrics you want to move,
then right click IN THE BAR LYRIC AREA of any highlighted bar, and select from the drop down, say "Cut selected bars".

That will remove the bar-based lyrics from the selected bars.
Next, highlight ALL the bars where you want the lyrics to be placed, and again, right click in the bar lyric area and select Paste.

The trick as you can see, is to right click not in the highlighted chord area, but above that in the bar lyric area.

The dropdown when you right click is somewhat misleading, as it implies it is going to (say) "cut" selected bars, when indeed it is only going to cut the bar-based lyrics, and not the bars themselves. (Although to be fair, the heading of the dropdown does say "Bar Lyrics".)

If I've misunderstood your question, let us know and we'll try to help you out.
Perhaps your step by step process would help.

Good luck!
LLOYD S