The hosts dominated possession but could not find the finishing touch against the Sicilian club, who defended well.
The result will not please Lazio coach Edy Reja, whose side have yet to win at home this season.
Lazio went into the game on the back of a midweek 2-1 win at Cesena, their first victory of the campaign.
Widely-travelled striker Djibril Cisse should have given Lazio a ninth minute lead when he got behind Senad Lulic's cross - but Palermo goalkeeper Alexandros Tzorvas kept out his right-footed strike.
In the 12th minute, Palermo had their first chance. Eran Zahabi fed Mauricio Pinilla inside the area and his shot was saved by Lazio keeper Federico Marchetti.
Shortly after the half-hour mark, Marchetti did well to clear Abel Hernandez's stinging drive from 30 yards.
Pinilla came close to giving the visitors the lead before half-time. The Chilean striker got his head behind Eros Pisano's cross and his effort went just wide of the far post.
Early in the second half, Cisse wasted a good chance to put the hosts in front, heading over the bar after Lulic had sent the ball into the penalty area.
Lazio continued to press forward and in the 57th minute Federico Balzaretti made a vital block from a goalbound shot from Miroslav Klose - and 11 minutes later Hernanes' curled free-kick was turned away for a corner by Tzorvas.
At the other end, substitute Josip Ilicic's bullet strike from outside the area was kept out by Marchetti.
With one minute remaining, Lazio should have broken the deadlock. Tzorvas failed to hold onto Klose's powerful strike and the ball fell to substitute Cristian Brocchi - but he fired wide from a good position.
However, Palermo held on for a point - their first away from home in Serie A this season.