The project was the brainchild of John Chadwick, who is best known for his work with Michael Ventris on the decipherment of the Linear B script. John was also deeply involved in lexicographic research: he worked on a number of projects, including the Oxford Latin Dictionary (1946-52), and he was one of the scholars supervising the Supplement to the large Greek-English Lexicon by Liddell and Scott (1979-93). His thoughts on Greek lexicography can be found in his book Lexicographica Graeca (1996). In 1998, he described the need for a new intermediate-level lexicon in an article for The Times.
The project was launched in 1998, with Dr Anne Thompson as Editor. Anne was a student of John Chadwick, and worked with him on a number of lexicographic projects, including the Liddell-Scott Supplement.
Professor James Diggle was first appointed as Principal Reader, and Chair of the Advisory Committee, to work in close contact with the writing team, reading and commenting on all pages of the lexicon as it is written. In recent years, however, he has himself been leading the team of writers and working full-time on the project. 
Fund-raising and administration were led by Professor Pat Easterling, the first Chair of the Management Committee, who was succeeded in 2009 by Professor Richard Hunter, the current Regius Professor of Greek, who is now Principal Investigator for the project.
In 1999, Anne Thompson held discussions with Professor Gregory Crane of the Perseus Project, which led to the creation of an electronic databank of lexicographic slips, designed by Professor Jeffrey Rydberg-Cox of the University of Missouri at Kansas City, which has become central to work on the Lexicon. At roughly the same time Dr Bruce Fraser
joined the project as Assistant Editor, and he is now, among other roles, the principal team member in charge of IT. In 2004, Dr Oliver Simkin, another Cambridge-trained linguist, joined us as Assistant Editor, followed in 2007 by Dr Patrick James. Dr Simkin moved in 2010 to take up a research post in Denmark, but has rejoined the project from 1 September 2014. At the same time the project has also been joined by two further Cambridge graduates, Simon Westripp,
who originally worked with the project as a undergraduate summer intern, and Dr Robert Crellin, who will work part-time as Assistant Editor. In 2002 Pauline Hire, formerly Classics Editor at Cambridge University Press, was appointed as project co-ordinator, giving general assistance where needed. Currently she organises the team of proof-readers, and herself shares in the reading.
Letters are now typeset and proofread as they become ready, rather than waiting for everything to be completed.
As of October 2014, 13 letters have been typeset and proofread (Chi, Delta, Eta, Nu, Omega, Psi, Rho, Sigma, Tau, Theta, Upsilon, Xi, Zeta); Iota, Pi and Phi are undergoing final revision prior to typesetting; Epsilon should be ready for typesetting by the end of 2014; Beta, Gamma, Lambda and Mu will be typeset in 2015; Alpha and Kappa by May 2016.
Delivery of final digital files to CUP is scheduled for summer 2016, with publication in 2017.