Camp Lawton was in Millen, Georgia. The following is here:

http://www.georgiaencyclopedia.org/nge/Article.jsp?id=h-3182

"When Sherman's Union army took Atlanta on September 2, 1864, Confederate prison authorities knew that Andersonville would be a prime target of any Union thrust into the heartland of Georgia, and they began moving Union prisoners of war to more secure locations. At Camp Davidson, constructed in July 1864 on the grounds of what had been the U.S. Marine Hospital in Savannah, prisoners were confined within a stockade that enclosed part of an orchard. The ample rations were a welcome respite from the horrors of Macon and Andersonville. The camp guards, the First Georgia Volunteers, had once been prisoners of war themselves. Because of overcrowding caused by the influx of Andersonville prisoners in September, a second Savannah prison, for officers, was set up on land adjacent to the city jail. Another stockade was hastily constructed for enlisted men. This structure, along with Camp Davidson, may have held more than 10,000 men, but both had to be abandoned after only a month and a half of use.

The most substantial prison holding former Andersonville captives was Camp Lawton in Millen, about forty miles south of Augusta. Camp Lawton was a stockade structure enclosing forty-two acres, making it the largest civil war prison in terms of area. Set only a mile off the Augusta Railroad, the pen was designed to hold up to 40,000 prisoners, although the population never grew to much beyond 10,000. By all accounts the prison at Millen was infinitely better than Andersonville. A generous spring ran north to south through the site, providing a fresh supply of drinking water. Rations were also more plentiful, since the countryside had yet to be scavenged of its food resources. Yet disease and death were not unknown, because many of the prisoners were terribly debilitated from their incarceration at Andersonville. During the short time the prison was open, from late September to early November 1864, nearly 500 prisoners succumbed to disease. As Sherman's troops approached Millen in the March to the Sea, the prisoners had to be moved yet again. A large portion of these were sent to South Carolina, and other groups were sent to Savannah."

The website has a picture of the camp.