Another way to do this if your song numbering is arbitrary, which I suspect it is, is to:
Run a query to export out the song ID, song name and song number fields. The song ID field is set when a song is added to the database and it will never change.
Import that into a spreadsheet and add a column for the new song number.
Go through and edit the spreadsheet putting in the new song number in the new column.
Import that back into the SQLite database as a temporary (should be deleted after) table
Run an update query on the songs table joined on the ID field to the temp table and update the song number in the songs table from the song number (that you edited) in the temporary table.
Delete the temporary table.
The query will run in less than a second and update the songs table in the OpenLP SQLite database.
Again you should make a copy of the OpenLP database to do this, if it is successful then you can simply replace the original songs.sqlite database. Of course also backup the original database.