Lev entered the music school for gifted children in Tiflis in the class of Anastasia Davidovna Virsaladze - herself a pupil of the renowned Anna Yesipova.
In 1948, Lev Vlassenko entered the class of Yakov Flier at the Moscow Conservatory and completed his undergraduate and postgraduate studies.
He and Chinese pianist Liu Shikun came second to Van Cliburn at the inaugural International Tchaikovsky Piano Competition in 1958.
He taught several world-renowned pianists such as Mikhail Pletnev, Victor Eresko,[1] Kalle Randalu, Mykola Suk, Lev Vinocour, Vladimir Daych, Gennady Dzubenko, Rena Shereshevskaya, Sergueï Kouznetsov, Natasha Vlassenko, Oleg Stepanov, Boris Petrov, Teofils Biķis, Karine Oganian, Jania Aubakirova, Justas Dvarionas, Alexander Strukov, Duncan Gifford and others.
At the Sydney International Piano Competition, the Lev Vlassenko Memorial Prize is awarded for the best performance of a virtuoso study.