Analysts and diplomats said the complex interplay of interests within the 148-member body, which sets the rules for the world's multi-trillion dollar trading system, made it hard to pick an early favourite in the race for the four-year post.
"I think it is just too hard to judge at this point," said former Canadian WTO trade envoy John Weekes, now an analyst with Geneva law firm Sidley, Austin, Brown and Wood.
Supachai stands down at the end of August, but the Geneva-based WTO is seeking to avoid the bitter feuding that accompanied the former Thai deputy premier's own selection.
The need for a smooth handover is heightened by the fact the WTO is in the midst of tough negotiations to liberalise world trade, the so-called Doha Round, with a potentially make-or-break ministerial meeting set for next December.
The candidates, who also include Brazil's WTO ambassador Felipe Seixas Correa and former Uruguayan trade envoy Carlos Perez del Castillo, will have three months to campaign before the head of the trade body's executive begins taking soundings on their support.
Under new rules, drawn up after the WTO failed last time to break a deadlock between Supachai and former New Zealand Prime Minister Mike Moore, the executive General Council should take a final decision at the end of May.
In 1999, such was the depth of the divisions cutting across developed and developing nations, the WTO opted to let both men serve three-year terms.
Yet unlike at the International Monetary Fund (IMF) or the World Bank, two other leading world financial institutions to which the WTO is often compared, the Geneva post carries no executive power.
"There is a contradiction between the importance members attach to the role of the director-general during the selection process and the tight leash they put him under once he is in office," said Weekes.
This has led some analysts to wonder how the energetic, confessed workaholic Lamy would deal with the potential frustrations of a job that calls more for behind-the-scenes cajoling than decision-taking.
Unlike in past succession battles, three of the candidates can be clearly identified with major negotiating blocs within the organisation, something that could favour the fourth - Perez del Castillo, a former General Council chairman.
Lamy was EU trade commissioner until last November, while Seixas Correa was spokesman for the Brazilian-led G20 group of developing countries, which also includes India and China.
Diplomats speculate that the United States, which has yet to declare where it stands, might be unwilling to see a WTO chief from Brazil, a country with which it has rowed fiercely over farm subsidies.
The Mauritian has the support of more than 50 states from the poor-nation African, Pacific and Caribbean (ACP) group, another bloc within the WTO.
"It may boil down to whether people go for the candidate with the least negatives, which could be Perez del Castillo, or they want a proven strong leader, and there Lamy may have the edge," said another trade analyst who asked not to be named.