Russia Today (RT) quoted family members as saying Lesin died of a heart attack on Wednesday.
RT quoted TASS as saying police had found no signs of foul play but that a formal investigation into his death had been launched.
A representative for Washington police was not immediately available to comment.
ABC said Lesin, who was Russia's Minister of Press from 1999 to 2004, has been accused of censoring Russia's independent media. He became head of Gazprom-Media Holding in 2013 but resigned the following year.