Lev Leshchenko was born on 1 February 1942 in Moscow, Soviet Union. His father, Valerian Andreyevich Leshchenko (1904–2004), was a Red Army officer who was at war outside of Moscow. He was awarded medals for his participation in the Second World War. His mother, Klavdiya Petrovna Leshchenko (née Fedoseyeva; 1915–1943), died shortly after Lev was born. His grandparents, along with his stepmother Irina Pavlovna Leshchenko, whom his father married in 1948, brought Leshchenko up in Sokolniki, Moscow. During his childhood, he was introduced to classical music and theatre, and began performing songs by Leonid Utyosov.
Between 1960 and 1959, Leshchenko worked as a stagehand at the State Academic Bolshoi Theatre, and before being conscripted into the army in 1961, he worked as an adjuster at a precision measuring instrument factory. Leschenko served in the mechanical vehicle division of the Soviet Army, positioned in the German Democratic Republic. On 27 January 1962, Leshchenko (then a private) became a soloist within the Soviet Red Army Ensemble, and received an offer to remain in the army. Leshchenko accepted every role offered to him by the ensemble, from singing in a quarter, conducting concerts and even reading verses, where it is said his entertainment career began. At the same time, he was preparing for the theatrical examinations of the Russian Academy of Theatre Arts (abbreviated as GITIS), the most respected theatrical school of the Soviet Union, which he passed and was successfully admitted to in September 1964.
Leshchenko began touring with concert bands, visiting some of the more isolated parts of the country. In 1969, Leshchenko was admitted as a member of the Moscow Operetta Theatre. He took up many minor musical roles, but was aware of his musical gift and was constantly looking for soloist acts. On 13 February 1970, having won a contest held by the state radio station, Leshchenko became a solo vocalist for the Soviet state radio station.
In 1975, Leshchenko performed "Den Pobedy", an immensely popular Soviet song dedicated to Victory Day, which was initially disliked by the authorities due to its unconventional music style. His rendition has become by far the most well known. In 1999 Leshchenko was given a star on the Star Square in Moscow.
In March 2014 he signed a letter in support of the position of the President of Russia Vladimir Putin on the Russian annexation of Crimea. For this he was banned from entering Ukraine. Crimea has been under dispute by Russia and Ukraine since March 2014.