The General Services Administration will begin design work this fall on a new federal courthouse in Greenville, S.C. After more than a year of deliberations, GSA picked a vacant lot across from the Greenville County Courthouse for the new facility, city officials announced Wednesday. The 204,000-square-foot facility will be more than three times the size of the current courthouse, which was built in 1937. The new courthouse was estimated to cost $135 million in 2007, according to local news website Journalwatchdog.com. Construction won’t begin until at least 2013, but Congress has already given the facility its new name. Lawmakers voted in…