One of the pioneers of 20th century New Zealand botany, Lucy Cranwell trained at Auckland University College (1925) and subsequently joined Auckland War Memorial Museum (1929-1944). It was during these years that she made extensive collections with L.B. Moore (1906-1987) and published on the New Zealand flora under the guidance of L.C. Cockayne (1855-1934). A grant from the Royal Society of New Zealand (1930) for an ecological survey of marine algae provided impetus for specialised research and collections, and specimens from these studies are also at BM. A trip to the 6th International Botanical Congress in Amsterdam (1935) introduced her to the new discipline of palynology and Professor E.J.L. von Post (1884-1951). He encouraged her to study subfossil material in the New Zealand peat strata which was the beginning of her move to palaeobotanical studies. In 1938 she visited Hawaii to join the Hawaiian Bog Survey of C.J.F. Skottsberg.

In 1943 Lucy married the American pilot, and later archaeologist, Captain Watson Smith (1897-1993) with whom she settled in the United States (1944). The vacant post she left in Auckland was taken up by her assistant Betty Molesworth, later B.E.G.M. Allen (1913-2002), another New Zealand plant collector with material at BM. Lucy became a Research Associate (1944-1950) in the Peabody Museum of Natural History at Yale University, continuing her palynological studies. From 1961 she worked as a Research Associate at the University of Arizona. A number of fossil taxa are named in honour of Lucy Cranwell, including the genus Cranwellia B.P. Srivast. Extant taxa include the labiate Stenogyne cranwelliae Sherff from Hawaii and the alga Gigartina cranwelliae A.R.O. Chapm. which is endemic to New Zealand.