The rank of Third Lieutenant has been used by the military at several points in U.S. history, especially during the Civil War. A brevet 2nd Lieutenant was often called a Third Lieutenant. During the War of 1812 the port guards - local yokels who volunteered to defend coastal cities where or near the city where they lived - who were selected were Third Lieutenants. They were numerous. As far as I am aware, they did not receive presidential commissions, certainly not always, and were somewhat analogous to a Warrant Officer today. However, they were considered part of the officer corps, and sometimes were promoted to higher rank. Perhaps, that is where the custom of referring to brevet Second Lieutenants as Third Lieutenants.
During the Civil War the title was widely used in the Union Army, again for volunteers who were selected to be trained as officers, and at least as of yet did not have a presidential commission. In the Confederacy Third Lieutenant was an official rank, the 0-1 rank of the CSA Army. This is a brief precis, but all I have time or energy for right now.