The Lake-men were the people of Esgaroth upon the Long Lake, south of Erebor. They were a trading people and before Smaug's coming they dealt with Erebor and Dale, and with the Wood-elves of Mirkwood.
The civil leader of the Lake-men was The Master of Esgaroth and he was chosen from among the old and wise.
As a trading people, the Lake-men knew the Common Speech, Westron. However, amongst themselves they spoke an ancient form of it, which was loosely related to but distinct from the also-ancient language of the Rohirrim. Tolkien "translated" Westron into English in his text, so to represent the ancient relative of it that the Rohirrim spoke, he substituted Old English. Thus, Tolkien substituted Old Norse for the language of the Lake-men (in person and place names, etc.) because it is an ancient relative of English that is related to Old English.