Needham is the son of Francis Needham, 5th Earl of Kilmorey, and Helen Bridget Fandel-Phillips, daughter of Sir Lionel Fandel-Phillips, 3rd Baronet.
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He attended Christ Church, Oxford, and in 1862 (aged nineteen), proposed to give a ball; this was prohibited by the college authorities, chiefly by Charles Lutwidge Dodgson (better known as Lewis Carroll).
In 1806 the changes in ownership of the Newry estates altered Corry's position; the lands had passed to a senior line of the Needham family and Lady Downshire, decided to return his brother General Francis Needham, 1st Earl of Kilmorey at the general election.