Lemurian quest are the pieces of paper in your inventory which act as side quest. They are in riddles so it's a little hard to decrypt them sometimes but the ones I did was;
Finn's Plight - simply complete the mission down the well after Finn joins your party.
Pastoral Panic - remember the pretty pink tree at the start of the game ? Once you finish Finns mission you will be tasked to go back there and clear out the spiders that lurk around it.
Bolmus Inferno - in the town of the Bolmus populi you will find a house with a rat inside. He will ask you to clear out his basement and fight a "dragon" that dwells inside. When you go down you will face Grim Reaper like creatures which are weak against water but usually have back up like the giants with stone on there back and the boulders so take out the reapers first and leave the giants till last. There are 2 reapers flying around and 2 In chest.