The cards copied show that he was a private in Company D, 24th Ohio Volunteers, which in 1864 was disbanded and personnel, along with men of Companies B,C, G, I, and K, 18th Ohio Volunteers, were consolidated to form the (new) Company D, 18th Ohio (Veteran) Volunteers.
From fold3, Mr. Lewis' pension cards show he had enlisted in Co. D, 24th Ohio on June 13, 1861, and served with that outfit for three years.
From the data you posted, on Jan. 19, 1864, he reenlisted for another three years. However, his regiment did not reenlist en masse, and was mostly discharged from service in mid-1864. He was not alone, as it was noted his company mostly reenlisted for the war...
Ohio in the War, page 172, 24th Infantry
He was transferred to the (new) Co. D, 18th Ohio Oct. 20, 1864 for the balance of his service.
And he was finally discharged Oct. 9, 1865 from Co. D, 18th Ohio:
From "Ohio at Shiloh..."
Ohio at Shiloh, Google books