Lebedev was born in Tartu into the family of an impoverished serf. In the 1820s, serfdom was abolished in his region and the young Lebedev got an opportunity to study at a nearby school. His artistic endeavours attracted the attention of the Count Pahlen, who sent Lebedev to the Academy at Saint Petersburg with a full scholarship. In the Academy, Lebedev studied under Maxim Vorobiev. In 1833, he got the major gold medal for the painting View of Ladoga.
In 1834, he travelled to Italy on a pension and was met by the Russian artistic colony there, notably the native Karl Brullov. Lebedev loved to paint Italy’s natural landscapes; his landscape paintings are full of coloristic contrasts. Notable paintings derived from this period are "Ariccia near Rome" and "View of Castel Gandolfo near Rome" Lebedev’s landscapes had an immediate success with the public. Tragically in 1837, Lebedev went to work in Naples, where an epidemic of cholera started. The artist became ill and died at the age of 26.