The lazy susan has been around longer then it's name. Most female servant were named susan which became synonomous with servant. So they named it lazy susan (servant).
The rotating tray, is the lazy reference, because servants didn't have to keep bringing different selections of food. Susan was a common servant name in the 1700's.
They call it the "lazy susan" due to a reference in Vanity Fair. Before that they were called dumbwaiters which is also applied for elevators for transporting food.