Born in Nova Gradiška, Lulić started playing football at his village's club NK Graničar Laze, before moving early to NK Mladost Cernik.[3] In 2010, he moved to NK Osijek. He made his professional debut during the 2012/13 season. His first goal came during the 2013/14 Prva HNL season. On 23 September 2014 he moved to Sampdoria.
On 30 August 2021 he returned to Italy and signed with Frosinone in Serie B.[4]
On 3 January 2024, Lulić signed a contract with Bari until 30 June 2026.[5]