Sir Lionel Henry Cust KCVO FSA (25 January 1859 – 12 October 1929) was a British art historian, courtier and museum director. He was director of the National Portrait Gallery from 1895 to 1909 and co-edited The Burlington Magazine from 1909 to 1919.
Cust was born in London in January 1859, the son of Sir Reginald Cust (1828–1912), a lawyer, and his wife Lady Elizabeth Bligh, daughter of the 5th Earl of Darnley. He was educated at Eton College and Trinity College, Cambridge.
In 1895, Cust married Sybil Lyttelton, daughter of George Lyttelton, 4th Baron Lyttelton and Mary Glynne. Her father´s family were prominent politicians and academics, and her maternal aunt was the wife of Prime Minister William Gladstone. They had one son.
In 1884 he joined the British Museum's Department of Prints and Drawings, at the suggestion of the Keeper Sidney Colvin. Unusually for a British scholar of his time, Cust had a predilection for the artistic schools of Northern Europe, not those of Italy. He compiled two catalogues of works on paper in the British Museum collection, in 1893 and 1896. Cust contributed a number of entries to Bryan's Dictionary of Painters and Engravers and the Dictionary of National Biography.
In 1895 he was appointed Director of the National Portrait Gallery, succeeding the founding director, Sir George Scharf. In the Portrait Gallery Cust's two strongest interests, in art and British nobility, converged. Cust was of aristocratic stock himself and his obituary in The Times described him as a "walking genealogy". During Cust's directorship the Gallery moved to its current premises on St Martin's Place in London.