Lukoszevieze has premiered and commissioned new works for cello by many contemporary composers, including Christian Wolff, Christopher Fox, Gerhard Stäbler, Amnon Wolman, Laurence Crane, Richard Ayres, Phill Niblock, Jennifer Walshe, Claudia Molitor, Arturas Bumšteinas, Ričardis Kabelis, Richard Emsley, James Saunders, Alwynne Pritchard, Peter Eötvös, Bryn Harrison, Karlheinz Essl and Zbigniew Karkowski.
Lukoszevieze is the only constant member, although other musicians have been regular members since the ensemble's formation, such as the pianists Philip Thomas & Kerry Yong, violinists Gordon MacKay, Mira Benjamin, viola player Bridget Carey, clarinettist Heather Roche and percussionist Simon Limbrick .
[6] The ensemble has commissioned over one hundred new works by international composers, given the UK premiere of over one hundred further works,[7] and performed at venues and festivals including Café Oto, the Serpentine Gallery, Queen Elizabeth Hall, Turner Contemporary, MaerzMusik, Wien Modern, Ultima, and Witten New Music Days.
[9] In 2015, 20th anniversary celebrations for the ensemble included a broadcast on BBC Radio 3, and concerts at the Huddersfield Contemporary Music Festival and London's Wigmore Hall, with commissions from composers Egidija Medekšaite, Leo Chadburn, Martin Arnold, Jobina Tinnemans, Vitalija Glovackyte and Cassandra Miller.
The ensemble has recorded many albums for the label Another Timbre, including discs of music by Linda Catlin Smith, Cassandra Miller, John Cage, Ryoko Akama, Georgia Rodgers, John Lely, Tim Parkinson, Luiz Henrique Yudo, James Saunders and Julius Eastman, besides albums of music by John Cage, Christian Wolff, Michael Parsons, James Weeks and Cornelius Cardew for labels such as Matchless, Metier and Setola di Maiale.