He fulfilled requirements for achieving highest chess title Grandmaster on 29 November 2020[1] when he was exactly 16 years, 10 months and 7 days old, becoming the first Serbian who managed to get such an achievement before 17th birthday.

In his first competitive season ever, Budisavljević won the first place at the Cadet Championship of Serbia, both in standard and rapid chess[2] and continued winning Serbian Championships in standard chess for next six years, achieving six times consecutive Serbian Cadet chess champion, as follows: BEST Results at European Chess Championships Participation at World and European Youth Chess Championships as invited player ― Champion of Serbia In January 2018, Luka exceeds 2300 rating points on January FRL and was awarded FIDE Master Title.

[20] In 2019 Luka wins 5 (five) IM norms for International Master Title: Luka exceeded 2400 rating points in October 2019 FIDE Rating List, fulfilling all requirements for International Master title, which was awarded to him by FIDE in 2020.

[26][27] On 29 Nov 2020 Budisavljević fulfilled the requirements for the Grandmaster Title[33] when he was exactly 16 years, 10 months and 7 days old.

In his age group[35] (chess players born in 2004), Budisavljević holds: At the end of 2021, before his 18th birthday on the rating list of Serbia chess players,[48] Budisavljević was at 9th position with 2511 rating points, and was one of the most active Serbian chess players with 109 standard chess rated games, on 12 tournaments, during the pandemic 2021 year.