Lanier (1842-1881), a native of Macon, was ahead of his time in that he believed the South should be less reliant on cotton, and he was a lover of the arts. I mentioned Lanier in a post I wrote in January after a trip to Asheville, NC, where I visited the Richmond Hill Inn, a place connected to Lanier (to refresh your memory on this, click here). Lanier's birthplace home is still standing in Macon and is open to the public for tours. I intend to get down there to check it out sometime this year. I can't find any information on Lanier's connection to Augusta, however.
Ryan (1838-1886) is nicknamed "the poet of the Confederacy" and "the poet of the lost cause." He intended to be commissioned as a military chaplain for the Confederate Army, but wasn't accepted. Instead, he came along anyway and ministered to sick and wounded soldiers and edited a publication in New Orleans. He wrote two poems as a tribute to his brother, a soldier killed in action. Other poems followed. He later lived and worked in Augusta and edited more periodicals.Randall (1839-1908) wrote mostly historical poetry, including what's referred to as the "unofficial anthem of the Confederacy," "Maryland, My Maryland." After the Civil War ended, he became a newspaper editor in Augusta.
Hayne (1830-1886) was called "Poet Laureate of the South" during his day. After the Civil War ended, he moved to Augusta and edited a newspaper for only three months.
There is very, very little information available about this monument and how it came about. The biggest article I've found through Google searching is here.