Lennox was the third son of Charles Gordon-Lennox, 5th Duke of Richmond, and Lady Caroline, daughter of Field Marshal Henry Paget, 1st Marquess of Anglesey.

According to John F. Beeler in British naval policy in the Gladstone-Disraeli era, 1866-1880, Lennox acted as a spy to the then Chancellor of the Exchequer, Disraeli, informing him of the intentions of leading admirals.

[7] He was forced to resign as First Commissioner of Works after revelations in the case of Twycross v Grant regarding the Lisbon Tramways swindle, of which company he was a director.

[8][9] Lennox married Amelia Susannah (née Smith, then Brooman), widow of John White, in 1883.

[1] John White was the uncle of another peer, Lord Overtoun, while lady Amelia was the great-grandmother of 1950s MP Richard Brooman-White.