The Scotsman won the 1999 Open at Carnoustie in an event many remember most for Jean van de Velde's triple-bogey at the final hole.
Lawrie prevailed in a playoff against Van de Velde and American Justin Leonard.
World number 67 Moore has played in eight British Opens, with a tie for 12th in 2014 his best result.
He played on the victorious 2016 U.S. Ryder Cup team.
He has won five times on the PGA Tour.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Christian Radnedge)
