Between 1921-1925, he studied at the Moscow Conservatory with the well-known tenor, Nazari Raisky (1875-1958). In 1924, he sang in the opera studio of Konstantin Stanislavsky. From 1926-1931, he sang in the theatres of Sverdlovsk, Harbin, and Tbilisi. In 1931, he was invited to the Bolshoi Theatre, where he sang the roles of Tsar Berendei (Snow Maiden), Lensky (Eugene Onegin), and Gerald (Lakmé). Along with his friendly rival Ivan Kozlovsky (1900-1993), he was the leading tenor at the Bolshoi until 1956.
While Lemeshev was one of the leading tenors of the Bolshoi Theatre, he was idolized by female fans who were jokingly called "lemeshistki." The theatre lobby was a venue for scuffles between the "lemeshistki" and the "kozlovityanki," as Kozlovsky's fans were known. 
Lemeshev's roles included Levko in May Night, Zvezdochyot (the Astrologer) in Golden Cockerel, the Indian guest in Sadko by Nikolai Rimsky-Korsakov, Boyan in Ruslan and Ludmila by Mikhail Glinka, Dubrovskiy in the opera of the same title by Eduard Napravnik, and the Duke in Verdi’s Rigoletto, among others. Lensky was his signature role, however, and he played it more that 500 times from 1927 onwards. He performed it for the last time on his 70th birthday, after suffering three heart attacks and having a lung removed.
Asteroid number 4561 received the name Lemeshev in 1978, a year after Sergei Lemeshev's death.
see the link for more information
Lemeshev: La donna e mobile. (Verdi: Rigoletto). Rec.: 1956. Source: Discovery Classics. File: mp3pro at 16 kbit/s. Size: 323 kb.
)“He sang sul soffio (leaning on the breath), avoided stressful abdominal respiration (only Caruso could do it), and directed the sound current to the mask, the method of singing which was so much Lauri-Volpi's gospel.” (Dr. Joseph Fragala, see the link
)