[2][3] Simonović played for the senior Yugoslav national basketball team that won the gold medal at the 1970 FIBA World Championship.

[4] Born in Vrnjačka Banja to parents Jevrem Simonović and Ilonka (née Dobai), both of whom worked as hairdressers, young Ljubodrag grew up in Kraljevo with an older brother Vladimir.

[5] Simonović's mother Ilonka, born in 1921, came from a mixed background, born to German mother Ana Schumetz and Hungarian father János Dobay (the surname was later spelled as Dobai), a left-leaning officer who participated in the ultimately unsuccessful 1919 Hungarian Revolution before fleeing over the border into the recently established Kingdom of Serbs, Croats and Slovenes to escape the White Terror of Miklós Horthy.

Simonović moved to Belgrade in 1967 at the age of eighteen in order to play for KK Crvena zvezda as the latest addition to a talented squad led by twenty-six-year-old Vladimir Cvetković with a slew of up-and-coming youngsters such as nineteen-year-old small forward Dragan Kapičić and eighteen-year-old mercurial point guard Zoran Slavnić.

Coached by Milan Bjegojević, Zvezda, somewhat improbably, won the 1968–69 Yugoslav League title in Duci's third season at the club.

[8] Among his many stellar displays throughout the season, one stood out — playing away at Hala sportova against the eternal crosstown rivals KK Partizan he scored 59 points.

Despite Simonović having an incident-filled summer with the national team at the 1972 Olympics, he was initially able to put it behind him and contribute greatly to Zvezda's European Cup run.

However, all was not well inside the Zvezda locker room as a simmering rift between local Belgrade-born-and-raised players who came up through the club's youth system (Slavnić and Kapičić) and those brought in from the outside (Simonović and Vučinić) had been gaining in intensity.

Cliques were being formed within the squad and things eventually boiled over on 10 January 1973 in Tel Aviv during the away contest versus Maccabi, the first game of the quarterfinals group stage.

Zvezda had been leading throughout the game with Duci pouring in baskets from all positions, however, he was not satisfied with the frequency and the quality of passes he is being fed by point guard Slavnić.

Deeply dissatisfied over what had transpired and extremely stung by the fine, right after playing a Yugoslav League game versus KK Željezničar Karlovac,[9] Simonović announced a decision to stop playing basketball, saying he would like to devote his time and efforts to science, having already been pursuing a master's degree in law after earning an undergraduate law degree two years earlier.

After his retirement from sport he has written various books, including: "Rebellion of Robots", "Professionalism or Socialism", "Olympic Deception of the 'divine baron' – Pierre de Coubertin.