The Atlanta Journal-Constitution first reported that Lambert had been named the starter.
Smart said Monday that both Lambert and Eason could play against the Tar Heels.
Lambert started 12 games for the Bulldogs in 2015, throwing for 1,959 yards with 12 touchdowns and two interceptions. Georgia went 10-2 in games that Lambert started last season.
Information from ESPN staff writer Edward Aschoff contributed to this report.