All about the island in Lake Woodlands - Mitchell Island All about the island in Lake Woodlands - Mitchell Island Hi friend. Today we have a fun topic at hand. If you have ever been to The Woodlands, or looked at a map of The Woodlands, you might have noticed that there is an island along the east shore of Lake Woodlands. The unofficial name of this island is Mitchell Island. There is much history to this island. In the early 1960's George Mitchell had decided to dip his company, Mitchell Energy (think oil & gas), into land development. Local brokers of Houston knew of his desire to diversify, and informed him of a possible deal. This deal would be the first 2,800 of the 27,000 he purchased to develop into The Woodlands you know today.