I do not find reference to a 3rd Lieutenant in this 1890 regimental history of the 1st iowa Cavalry
The "Iowa City Cavalry Company" was enrolled principally in the counties of Johnson and Washington, and organized at Iowa City, with James O. Gower as Captain, afterward
Major and Colonel ; J. R. Elliott First and P. E. Shaver Second Lieutenants. The following history as to the organization has been furnished by Surgeon M. B. Cochran : "On the 28th of March, 1861, a meeting was held in Mendenhall s hall, Iowa City, to take measures to organize a company of cavalry.
The meeting adjourned to the 15th of April, when another meeting was held in Market hall. Thirty-five names were enrolled and an organization was completed. J. O. Gower way chosen Captain,
J. W. Porter First Lieutenant, John Borland Second Lieutenant, and J. R. Elliott Orderly Sergeant, The company met for drill regularly from that time until it was ordered into quarters by the Governor.
"A history of the First Regiment Iowa Cavalry Veteran Volunteers : from its organization in 1861 to its muster out of the United States service in 1866 : also, a complete roster of the regiment"
Lothrop, Charles H. (Charles Henry), 1831-1890; Lothrop, Virginia, Publication date 1890
The Confederate Army did employ a 3rd Lieutenant, also called Jr. 2nd Lt. or Brevet 2nd Lt.
Nowhere however, have I been able to define the duties of an Infantry Lieutenant other than assist their Captains “ . . . in the performance of all company duties.”