Instructions
Accept the "Fremennik Trials" quest from Brundt the Chieftain in Rellekka. He resides in the longhall. Go east to the woods, then use the hatchet to chop a branch off of the "Swaying Tree." Use a knife on the branch to carve a Lyre. You'll need 40 Crafting skill to do this; you can get those by drinking a Potion of Crafting.
Go southeast to find a pasture. Talk to the troll there and he will (eventually) ask you to make him some stone soup for a reward. Use his pet rock, potato, onion, and cabbage on his cauldron to produce this soup, and he'll give you some golden wool. Go west to the Seer's Village to use their loom to spin the fleece into a ball of yarn.
String the lyre by using your Fletching skill (which can be boosted by using a Potion of Fletching) and you'll have a normal lyre. To enchant, head southwest of Rellekka, then fish off the pier for a shark, manta ray or sea turtle. Offer the raw flesh to the nearby shrine and your lyre will be enchanted.