Lubimov was born in Moscow in 1944. He studied at the Moscow Central Music School and entered the Moscow Conservatory in 1963; his teachers there were Heinrich Neuhaus and Lev Naumov. His interests there included both Baroque music and 20th century music as well as conventional repertory. In spite of disapproval from Soviet authorities, Lubimov gave the Soviet premieres of works by Charles Ives, Arnold Schoenberg, Karlheinz Stockhausen, and other members of the 20th century Western avant-garde. As a result, he was banned from traveling outside the Soviet Union for some years. Instead, he developed his abilities in playing period instruments and in historical performance practice, both rare in the Soviet Union at the time. He founded the Moscow Baroque Quartet and co-founded the Moscow Chamber Academy, and he organized an avant-garde music festival called Alternativa. In 1990, playing fortepiano, Lubimov began releasing a complete cycle of Mozart's keyboard sonatas on the Erato label.
Lubimov went on to record for a great variety of other labels, including BIS, Zig Zag Territoires, and Alpha. He has issued recordings of music by John Cage and other 20th century composers on the ECM label. Lubimov has been in demand as a concerto soloist, appearing with such groups as the Orchestra of the Age of Enlightenment, the London Philharmonic, and the Finnish Radio Symphony Orchestra, with which he toured Europe, performing Rachmaninov's four piano concertos. He is active as a chamber music player, performing with such notable partners as violinist Christian Tetzlaff, viola da gamba player Wieland Kuijken, and tenor Peter Schreier. Lubimov has continued to record prolifically, and by the early 2020s, his catalog comprised well over 50 albums. In 2022, he issued an album of music by Valentin Silvestrov on Erato and the album John Cage: Four Walls on the Fuga Libera label. That year, he was arrested as he finished an antiwar concert in Moscow. ~ James Manheim, Rovi