Cox was born to parents who worked as government servant in the Post Office telephone engineers' department. When he was just a few years old Cox moved to Harringay, where he at six he started attendance at the South Harringay County School. In 1909, he entered Owen's School in Islington, one of the old London Grammar schools.
Dr. L.R. Cox is one of the leading authorities on fossil Lamellibranchiate and Gastropoda. His work at the British Museum has enabled him to study material from almost all parts of the world, and the results of his researches have been published in the transactions of learned bodies in at least ten countries. Although his contributions to Mesozoic and Cainozoic Palaeoconchology are widely recognised as important and sound, his work on the Jurassic Lamellibranchiata is outstanding.
In addition to his systematic studies, he has made illuminating researches of an historical kind, especially in respect of the life and work of William Smith.
The fauna of the basal shell-bed of the Portland Stone, Isle of Portland.// Proceedings of the Dorset natural-historical and archeological Society, 1925.– Vol. 46.– p. 113-172, pls. 1-5.
Synopsis of the Lamellibranchia and Gastropoda of the Portland beds of England. Part I.// Proceedings of the Dorset natural-historical and archeological Society, 1929.– Vol. 50.– p. 131-202.
Fossil Mollusca from southern Persia (Iran) and Bahrei Island.// Memoirs of the Geological Survey of India. Palaeontologia indica, 1936.– N. S., vol. 22, mem. №2.– ii+69 pp., 8 pls.
A survey of the Mollusca of the British Great Oolite series primarily a nomenclatorial revision of the monographs by Morris et Lycett (1851-1855), Lycett (1836) and Blake (1905-1907). Part II.// Palaeontographical Society. Monographs, 1950.– Vol. 105, №449. – p. 49-105. (together with W. J. Arkell)
Cretaceous and Eocene fossils from the Gold Coast.// Gold Coast Geological Survey. Bulletin, 1952.– №17.– 68 pp., 5 pls.
The British Cretaceous Pleurotomariidae.// The Bulletin of the British Museum (Natural History). Geology, 1960.– p. 385-423, 1 fig., pls. 44-60.
The molluscan fauna and probable Lower Cretaceous age of the Nanutarra formation of Western Australia.// Department of National Development. Bureau of Mineral Resources, Geology and Geophysics. Bulletin, 1961.– №61.– 53 pp., 1 fig., 7 pls.
Jurassic Bivalvia and Gastropoda from Tanganyika and Kenya.// Bulletin of the British Museum (Natural History). Geology, 1965.– Suppl. 1.– 213 pp., 2 figs., 30 pls.