GREENBRIAR, TEXAS. Greenbriar is on Lake Greenbriar just west of Tyler in central Smith County. State Park Road 164 runs along the lake's western shore, and the St. Louis Southwestern Railway runs just north of the lake. The 1936 county highway map shows one business and a cluster of farms at the community. In 1976 Greenbriar had fifteen homes accessed by dirt roads, and by 1985 the Briarwood Country Club had been constructed.