Think of these three ranks: Captain, Colonel, General. They each need an assistant, someone to "act in their place": a "lieu-tenant." So, we have a Lieutenant standing in for a Captain, a Lt. Colonel in lieu of a full Colonel, and a Lt. Gen. acting for a full General.
"Major," according to them, derives from the antiquated "Sergeant Major," and would be an even more junior assistant: a Sgt. Maj. reporting to a Lt., a Major to a Lt. Col., and a Major Gen. to a Lt. Gen.