Alexandra was born in Bucharest, Romania. From 1965 to 1971, she studied at the Ciprian Porumbescu Conservatory (now the National University of Music Bucharest) under Tudor Ciortea and Tiberiu Olah and took composition courses in 1974, 1978, 1980 and 1984 in Darmstadt, Germany. She had a doctorate in musicology and taught composition, orchestration, and music analysis at the Conservatory from 1971 until her death in 2011.
A prolific composer in the neoromantic style, Alexandra had over 100 of her works performed and published in Romania. According to musicologist Octavian Cosma, she was "in her element with orchestral and chamber music, employing repetitive and evolving techniques, with melodic lines which suggest lyricism and meditation" and an instrumentation that used "a palette of delicate, pastel colours." Alexandra married the Romanian cellist and composer Şerban Nichifor in 1978. They performed together as Duo Intermedia from 1990 and were co-directors of the Nuova Musica Consonante - Living Music Foundation Festival.
Liana Alexandra died at her home in Bucharest of a cerebral hemorrhage at the age of 63. On 12 January 2011, two days after her death, the broadcast Univers muzical românesc on Radio România Muzical was dedicated to her. In May of that year, Liana Alexandra: Marturii despre muzica ei (Liana Alexandra: Confessions about her Music) was published by Editura Stephanus in a bilingual Romanian and English edition. Edited by Şerban Nichifor, the book is an anthology of writings on Alexandra's music by composers, critics and musicologists including Viorel Cosma, Grete Tartler, Robert Voisey, and Jacques Leduc. Later that month, her 1987 opera În labirint (The Maze) was performed in her memory by the Banatul Philharmonic of Timișoara as the closing concert of the Timișoara International Music Festival (31 May 2011)