GNU Parted is free software, covered by the GNU General Public License Version 3, or (at your option) any later version. This should have been included with the Parted distribution, in the COPYING file. If not, see <http://www.gnu.org/licenses/>.
Libparted is considered part of GNU Parted. It is covered by the GNU General Public License. It is NOT released under the GNU Lesser General Public License (LGPL).