He graduated from opera directing at Prague's Music and Dance Faculty of the Academy of Performing Arts. From 1999-2016 he worked at the Prague State Opera and the National Theatre, working with many foreign directors.
He was the Head of the State Opera Arts Administration between 2013– 2016. He was the Head of the Opera of the Silesian Theatre in Opava between 2017– 2019. Since January 2021, he has been appointed director of the Slovak National Theatre Opera in Bratislava.
In 2009 he staged a reconstruction of Dominik Neuner's original 1991 production of Verdi's Otello at the Prague State Opera, and in 2011 he directed a new production of Verdi's Il Trovatore.
He produced Jan F. Fischer's opera The Games for the Prague Children's Opera in 2003 and two years later Benjamin Britten's opera The Little Sweep using his translation and lyrics. In 2011, he was invited to stage another production of this Britten title at the National Moravian-Silesian Theatre in Ostrava.
In 2006 he directed a scenography reconstruction of Mozart's opera Don Giovanni for Opera MozArt at The Estates Theatre in Prague.
Lubor Cukr has also been active abroad (Opéra de Nice, Opéra de Toulon). In 2008 he directed Mozart's opera The Marriage of Figaro at the Opera de Nice. With the conductor Robert Jindra, he also staged the award-winning production of Richard Wagner's first opera, Die Feen [The Fairies], at the State Theatre Košice, which ranked 3rd place in the Opera Slovakia poll in 2017 and also received a nomination for the Dosky Award.
He has been a member of Académie Desprez, association française pour le rayonnement du Théâtre du Château de Drottningholm et du Musée Suédois du Théâtre since 2003. He was involved with the Pardubice Conservatory from 2013– 2017, and since 2011 he has been associated with the Music Academy Prague.
At the Silesian Theatre in Opava, he directed Mozart's opera La clemenza di Tito [The Clemency of Titus] (2010), Dvořák's The Devil and Kate (2013), Tchaikovsky's Eugene Onegin (2014), Mascagni's Cavalleria rusticana (2016), Orff's The Wise Woman (2017), Verdi's Falstaff (2017), Gluck's Iphigenia in Tauris (2018), Smetana's The Bartered Bride (2018), and Weber's The Sorcerer (2019).
At the Moravian Theatre Olomouc, he created an opéra-comique production, The Bells of Corneville (2020), by R. Planquette to celebrate the 100th anniversary of the foundation of the theatre. He has staged a new production of Tchaikovsky's opera Eugene Onegin for the South Bohemian Theatre in České Budejovice (2021).