Maine is a province in france; The Caspian is far larger than lake Baikal in terms of volume, you should probably specify you mean freshwater lakes only; Olivenca should be accepted for Olivenza as that is the Portuguese name for it
Olivenca is now an accepted answer and the question now specifies freshwater lakes, but the French province of Maine is now part of the departments of Sarthe and Mayenne in Pays de la Loire and not its own province.