Lazić made his professional debut for Red Star Belgrade on 26 May 2013, in a Serbian SuperLiga match versus Vojvodina.
On 23 June 2015, Lazić signed a four-year contract with Russian Premier League side Anzhi Makhachkala.
On 11 January 2019, Lazić signed a one and a healf-year contract with Bosnian Premier League club Sarajevo.
[6] Three days after the cup final, on 18 May 2019, Lazić also won the league title with Sarajevo after the club beat Zvijezda 09 4–0 at home.
[9] On 20 October 2020, Lazić returned to the Serbian SuperLiga, joining Radnički Niš.