Polling stations across the country opened at 06:00 am (0500 GMT) for the first round of voting, and were scheduled to close at 08:00 pm (1900 GMT).
Some 47,000 council seats are up for grabs, as well as 2,500 mayorships from village level through to the high-profile job at Warsaw city hall.
Lech, who is Poland's president, and his identical twin brother Jaroslaw, the prime minister, helped sweep a corruption-tainted left-wing government from power in parliamentary elections in September 2005.
Analysts say that the local vote will help the fractious governing coalition -- made up of the Kaczynskis' Law and Justice (PiS) party, the populist Samoobrona party and the deeply Catholic, far-right League of Polish Families -- test its muscle against its opponents ahead of a potential snap parliamentary election.
Sunday's vote largely pits the government bloc against two other camps: the liberal Civic Platform and its Peasants' Party (PSL) allies, and an unprecedented coalition of ex-communists and former anti-communist dissidents from the Solidarity movement.
Some 30 million Poles are eligible to vote but turnout has barely reached 40 percent in recent years.
Exit poll results are expected on Sunday evening, but the first official figures are unlikely to be known until Monday morning, according to the national election commission.
A run-off round will be held on November 26 for any seats and mayorships which have not been won on Sunday.

Copyright AFP (Agence France-Presse), 2006