Born in Milan, Lazzari started his professional career at hometown club Atalanta. During 2003–04 Serie B season, he was promoted from Primavera under–20 team to the first team. He made his Serie B debut on 4 October 2003, substituted Riccardo Montolivo in the 86th minute. He followed the team promoted back to Serie A as the 5th and made his Serie A on 22 September 2004, replaced Nicola Mingazzini in the 81st minute. Lazzari scored a hat-trick against Juventus in Coppa Italia, a match in which Juventus was eliminated in a 5–3 aggregate, while Lazzari also scored the 2 goals in the first leg. Lazzari followed Atalanta relegated back to Serie B in June 2005. He won Serie B champion with the team in June 2006.
In August 2006, he was loaned back to Serie B for Cesena, as part of the deal that Atalanta signed Adriano Ferreira Pinto. On 31 January 2007 he was sub-loan to Piacenza Calcio, as part of the deal that Cesena signed Alessandro Pellicori. In July 2007, he was loaned to Serie B newcomer Grosseto, where he finally became a regular starter and scored 9 goals.
On 9 July 2008, he was sold to fellow Serie A side Cagliari in co-ownership deal, in a 4-year contract, for €1.8 million fee. He took no.10 shirt from departed winger Pasquale Foggia but started occasionally. He became a regular starter in 2009–10 season, after Andrea Cossu became the first choice attacking midfielder, with Lazzari acting as left midfielder. He scored 6 goals that season. On 3 June 2010, Cagliari decided to sign him outright for another €2 million.
In July 2011 Lazzari was signed by ACF Fiorentina in another co-ownership deal, for €3 million, in a 4-year contract. In June 2012 La Viola acquired Lazzari outright for another €1.638 million.
On 30 August 2012 he was official loaned to Udinese.
With his new team, on 2 September 2012, he scored the 1–4 goal against Juventus at Stadio Friuli. The loan was renewd for 2013–14 Serie A season.
In the Europa League qualifying round match against Bosnian club Široki Brijeg in August 2013, Lazzari scored from the halfway line as Udinese won 4–0.
Lazzari played 3 times for La Viola in 2014–15 Serie A.
In summer 2015 Lazzari was signed by Carpi F.C. 1909 in a 1-year contract as a free agent.
On 1 February 2016 Lazzari was signed by Bari, with Filippo Porcari moved to opposite direction.
He was an unused member of Italy U21 team at 2007 UEFA European Under-21 Football Championship.