The Lonely Mountain is a Mountain east of Mirkwood, very near Laketown. It is all by it self, hence it's name "The Lonely Mountain"
Dwarves lived in the Mountain untill a dragon named Smaug invaded and killed all the dwarves but Thror, Thrain, Thorin and a few others. During Bilbo's adventure near the end the dragon was slain by Bard the Bowman, and the dwarves reclaimed their land. They also claimed all the dragon's riches, much to the anger of The Men of Laketown and the Elves of Mirkwood. A war was brewing between the three, fortunately they united and defeated a army of goblins, led by Bolg son of Azog, before they came to blows with each other.