After you avenged Lilly's death and finished A Song Of Vengeance, you can talk to the composer:
In search of a song
Well you've proven to be quite the apprentice. I'm proud to have taken you under my wing, though there is still more to do if you are interested.
A few years ago I was caught up in a huge storm at sea. I survived but the storm sucked up years of songwriting and scattered them across the world.
If you happen to come across my lost songsheets, bring them to me and I will reward you for every five you turn in. I have a good stash of rewards so keep bringing me more and I will continue to reward you.
Now on with you, I've got music to compose...
The Lost Song Sheets will start to appears on dead pirates and inside their pirate chests. Every 5 of it can be turned in to the Composer for a random reward. This process is random and can be repeated infinitely, so it's possible to have multiple duplicate items.