Popova was born in Ivanovskoe, near Moscow, to the wealthy family of Sergei Maximovich Popov, a very successful textile merchant and vigorous patron of the arts, and Lyubov Vasilievna Zubova, who came from a highly cultured family. Lyubov Sergeyevna had two brothers and a sister: Sergei was the eldest, then Lyubov, Pavel and Olga. Pavel became a philosopher and the guardian of his sister's artistic legacy. She grew up with a strong interest in art, especially Italian Renaissance painting. At eleven years old she began formal art lessons at home; by the age of 18 she was studying with Stanislav Zhukovsky, and in 1908 entered the private studios of Konstantin Yuon and Ivan Dudin.