Lord Palmerston, also known as Henry John Temple, was a British statesman who served twice as Prime Minister in the mid-19th century. As a key figure in British foreign policy, he was very concerned about Russia`s intentions towards the British Empire, specifically the Indian subcontinent.

Option 1, Lord Auckland, was the Governor-General of India during the same period, but the quote does not align with his views. Similarly, option 3, Lord Canning, although he was a British statesman and Governor-General of India, he did not hold these views. Option 4, Alexander Burnes, was a Scottish traveler and explorer who worked for the East India Company, not a policymaker.

So it was Lord Palmerston (option 2) who believed Russian designs were `an imminent peril to the security and tranquility` of the Indian Empire in 1836, expressing his fear of potential Russian expansionism.