It depends on what you are doing to edit the MP3. Basically, as long as you don't alter the timing (edit the start point, edit out sections in the middle etc.) you should be able to do this.
Edit the file. Give it a new name. Place it in a new folder with the old original file (no text file if you already embedded the lyrics). Open the old file in QMIDI, and edit the karaoke file. The program will prompt you to save the lyrics before you can edit. Do a 'Save As...' and save as the new file's name. Now open the new MP3 in QMIDI, and lyrics should be synced. Do an 'Export Current' and replace the new MP3 with the same name. This will embed the lyrics.
Remove the new file from the folder and rename it to the original file's name. Put back where it used to be.
Should work. Let me know if any of this is wrong. The main difference I have with your system is, I always embed the lyrics (Export Current...) in the MP3 itself, so I don't need the text file.