Luchkevych is a son of Ukrainian international player and current coach Ihor Luchkevych and product of FC Metalurh Zaporizhya youth sportive school system. In December 2013 he signed a contract with FC Dnipro Dnipropetrovsk.[2] He made his debut for FC Dnipro in the match against FC Karpaty Lviv on 10 August 2014 in the Ukrainian Premier League.[3]
On 30 January 2017, Luchkevych signed for Belgian club Standard Liège.[4] On 12 March 2017, he made his debut for the club coming on as a substitute in a 55th minute in a Belgian First Division A match against Oostende.[5] On 13 May 2017, he scored the first goal for his club in a Europa League play-off match of Belgian First Division A against Mechelen.[6]