The Lake Monster is a quest in Dream World. It'll be the first quest, after entering Lakeview. First talk to the Chieftain, she tells you to find the Lake Monster in the last area of The Marsh. This will be told to you after talking to the village chief in Lakeview.
As soon as you reach level 6 you get the option "Seek" at The Marsh. This will make you fight the Lake Monster. After defeating him, return to the Chief. Quest complete!
"Hello . Thank you for killing that monster... your kindness will not be forgotten. " - Chief Leana
"I heard from Sheriff Graham of Junkton that evil is brewing in Emerald City, the lovely capitol of Dream World. Maybe this is why you have been called to this world. Please talk to the sheriff in Junkton before visiting the Emerald Princess."- Chief Leana