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Background
Dandelion will give you this quest when you talk to him in the New Narakort Inn (#1), provided that you can beat him in the drinking game. You can also trigger the quest by picking up
Dandelion's Lute at the merchant's house (#2).
Walkthrough
If you start the quest by meeting up with Dandelion, then he'll tell you the sad story of his lute -- how he had to leave it behind in a merchant's house (#2) after the merchant discovered him giving "lessons" to his daughter Rozalind. Since the merchant now wishes him bodily harm, Dandelion will ask you to fetch the lute back for him.
When you reach the house, the merchant will demand that you leave Rozalind alone, and you'll either have to bribe him or box him to get inside. Upstairs in the Rozalind's bedroom, after talking to Rozalind (and perhaps sleeping with her), you'll find
Dandelion's Lute in a trunk.
When you deliver the lute to Dandelion, he'll reward you with 5000 experience points, and then the next time you enter the inn during the evening hours, you'll witness Dandelion giving a performance for the townspeople.
1 - New Narakort Inn
2 - Merchant's House