Lehtonen, coming off a 6-0 win over Florida on Saturday, has five career shutouts. He has allowed two goals in three games this season.
Kozlov put Atlanta ahead 1-0 from the right circle at 12:26 of the first. The goal came after Tampa Bay defenceman Paul Ranger mishandled the puck in the Lightning zone.
Marc Denis made 19 saves for Tampa Bay, which has lost two straight at home.
Lehtonen stopped three shots - including an in-close chance by Martin St. Louis - during a 5-on-3 power play that lasted two minutes in the second. He also made a strong glove save on Vaclav Prospal's shot right after the man advantage ended.
The Lightning outshot Atlanta 17-4 in the second and 28-10 overall through two periods.
Tampa Bay went 0-for-6 with the man advantage and have converted one opportunity in 19 tries this season.
The Thrashers failed on three power-play chances. Their first opportunity in the second period lasted four seconds.
Notes: Tampa Bay C Andreas Karlsson (groin) missed his second consecutive game. . . . Atlanta has outscored its opponent 5-0 in the first period this season. . . . The Lightning have allowed five goals in the first while not scoring.