Michael,I am using Finale 2001, so my answer may not be valid for Finale 98. The reason why the result has the lyrics lower on the page is that the lyrics copy is put in a new verse. If the original is in verse 1, the copy will be put in verse 2, and the next paste is put in verse 3. The baseline for verse 2 is lower than the baseline for verse 1. And the baseline for verse 3 is lower than the baseline for verse 2. To edit lyrics in verse 2 you have to switch to verse 2. And to edit lyrics in verse 3 you have to switch to verse 3.
To get the baseline the same in all verses, go to
Lyrics menu > Adjust Baselines...
To switch to another verse, go to
Lyrics menu > Specify Current Lyric...
If the editing that you want to do in the pasted lyrics is only setting the baseline to the same vertical position as the original, you could just as well try a different solution: give up the copy-and-paste, and use drag-copy instead. When you drag-copy, the pasted lyrics is mirrored, i. e. there is only verse 1, but it is displayed in two places. If you edit the original lyrics, the mirrored lyrics will change as well.
Peter