UPDATE
I managed to solve this problem albeit it involves using a third-party software. I bought this sometime ago while I was experimenting with jailbreaking, and just realized I could use this to solve our problem. I updated it to the latest version. FYI, no jailbreak needed.
1) You will need a paid copy of
DiskAid 5.0
2) Open the app, and you should see this screen.
3) Connect your phone with the USB 30-pin connector to your computer (where your iTunes library resides.) while DiskAid is running.
4) You should see the screen of DiskAid changes from the top to this:-
5) Now navigate to File System>Media>iTunes_Control>iTunes
6) You should see
MediaLibrary.sqlitedb. This is the SQL database for all your media content on your phone. Click and hold it, drag it somewhere to your desktop to make a backup. You shouldn't be using it again if this process works out right. After you have done this, delete
MediaLibrary.sqlitedb from your phone. Just right-click and choose "Delete". Another copy of this file will be recreated by iTunes during the following steps.
DON'T WORRY!. If you are to open the Music app on your phone at this point, you will notice it shows no music on your phone. Don't worry, your music are still in your phone. Your phone just doesn't know it since it is missing the media database. We will now regenerate an updated media database from iTunes.
7) Now go to iTunes, and under "Devices" section, choose your phone.
8) Click on the "Music" section of your phone, and play (double-click)
ANY songs on your phone.
9) Something mysterious will happen! Yes you can see iTunes is syncing with your iPhone!!
10) Once the syncing is completed, unplug your phone from the 30-pin connector, and check your music from the Music app of your iPhone. You may have to wait awhile for the phone to process the new database. The lyrics
SHOULD be updated, at least mine did.
What this accomplishes is it forces iTunes to update the media database on the phone so that all the tags are synced. If you are to connect your phone to your computer again and navigate via DiskAid to the above-mentioned location, you will see the updated copy of MediaLibrary.sqlitedb.
Tested on an iPhone 4S running iOS 5.0.1 and iTunes 10.5.1. YMMV.