MuseScore allows moving a line of lyrics up or down. Start by selecting a word in the last line of lyrics. Right-click on it and chose "Select > More..."
This will bring up a dialog like the following:
Check "Same subtype", which will have the current verse specified by default, and click OK.
Bring up the element inspector, which will appear in the right side of the window. Use "View > Inspector" to make it visible if necessary. Under the "Lyrics" portion of the inspector, you will see information like this:
Increase the verse number by one. You can do this simply by clicking the upward-pointing triangle. The lyrics will move downward by a line.
Repeat for each verse in descending order until you have an open blank line where you want the new verse.