Born in Bucharest, Lucescu made 249 appearances in the Divizia A for Sportul Studenţesc, Naţional Bucureşti, Braşov, Rapid Bucureşti and Bacău.
He began his coaching career with FC Braşov in the 2003–04 season spanning 15 matches in the first league.
In June 2004, he was named coach of Rapid Bucharest. In his first season, he qualified for the UEFA Cup, finishing third in the domestic league.
In the 2005–06 season, he had a dramatic start of the season, being dismissed for one night, before the owner of the club, George Copos, decided to take him back. Lucescu and his side managed to defeat teams such as Feyenoord Rotterdam, Shakhtar Donetsk (his father's team), Hertha Berlin and Hamburger SV, reaching to the quarter-finals of the UEFA Cup. Rapid was taken out by city rivals Steaua Bucharest after two draws. In the league, he finished as runners-up, after being sixth at the half of the season.
The 2006–07 season was not as good. Rapid got eliminated from the UEFA Cup group stages after 4 draws, finishing fourth. However, in 2007 Lucescu decided not to continue with Rapid, after a fallout with some of the supporters and several disagreements with the club owner. He opted to return to Braşov.
Răzvan won the Romanian Cup with Rapid in 2006 and 2007, both leading Rapid into the UEFA Cup.
Lucescu decided to start all over and, instead of accepting to manage bigger clubs from abroad, he decided to coach Braşov, who relegated two years before and finished 10th in the last season of the second division. He didn't disappoint and won promotion from the first place. Bringing Braşov back in the first league.
On 29 April 2009, he was appointed head coach and general manager of Romania, leaving Braşov after a ninth-place finish in the first division and replacing Victor Piţurcă in this position. After two years in control he gave up the national team, following the 3–0 victory over Bosnia and Herzegovina, leaving it with chances of qualifying to the UEFA Euro 2012.
In June 2011, Lucescu returned to Rapid for a second spell as coach. Lucescu's Rapid side defeated Polish champions Śląsk Wrocław 4–2 on aggregate in the play-off round to qualify for the UEFA Europa League group stage. The club finished fourth in Liga I and reached the finals of the 2011–12 Romanian Cup.
On 31 May 2012, he was appointed at the helm of Qatari side El Jaish on a two-year deal. In his first season in charge Lucescu won the 2012–13 Qatari Stars Cup and led his side into the knockout stages of the AFC Champions League. His contract with El Jaish was terminated in January 2014 and he was replaced by coach Nabil Maâloul who led the club to the runner-up spot in the Qatar Stars League.
In March 2014, he was named the head coach of Liga I side Petrolul Ploiești replacing Cosmin Contra. He was sacked six months later, Petrolul finished third in the domestic league and were knocked out in the semi-finals by Astra Giurgiu in the Romanian Cup and also eliminated in the play-offs of the Europa League.
On 24 September 2014, Lucescu signed a one-year contract with Greek Super League club Skoda Xanthi. He guided them to their first Greek Cup final in their history.Național București
Romanian League Runner-up: 1996–97
Romanian Cup Runner-up: 1996–97
Romanian League: 2002–03
Romanian League Runner-up: 2005–06
Romanian Cup: 2005–06, 2006–07; Runner-up: 2011–12
Romanian Second League: 2007–08
Qatari Stars Cup: 2012–13
Greek Cup Runner-up: 2014–15