The stakes are higher than usual this year: Hyundai is trying to ditch its decades-old seniority-based wage structure, which has helped make its domestic auto workers its highest paid globally, with one based on merit.
Hyundai, which with sister firm Kia Motors is the world's fifth-largest car maker, argues that wages have reached a "critical limit" and it could become impossible to make cars locally. The union rejects the proposal, and neither side expects a resolution anytime soon.
Pressure is building from some members to strike again after the union and management failed to settle a dispute over base wages used to calculate overtime allowances and other payments by the end of March, as had been agreed by both sides.
"Discontent and distrust of Lee are running high among union members," said Ha Boo-young, an Ulsan factory worker who leads a centrist faction and lost to Lee in a run-off election in 2013.
"The incumbent union leadership has cozy relations with the company."
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Hyundai declined to comment on the union leadership.
Ulsan to Detroit
Lee's pragmatic approach was reinforced by a 2010 visit to Detroit, the U.S. city devastated by the "hollowing out" of its auto industry, which he warned was a cautionary tale for Ulsan, the southeastern Korean city where Hyundai's carmaking complex is the world's largest.
"As a Korean raised in a rural village with an illusion of the American dream, I came back to Korea with a small shock," Lee wrote in a union newspaper.
South Korea became an export powerhouse as a low-cost manufacturer of cars, electronics, ships and chemicals, but faces increasing competition from China and even Japan as costs rise.
Hyundai opened its Ulsan complex 47 years ago, but has not opened a new domestic factory since 1996, even as it builds plants overseas.
Lee, 54, who joined Hyundai in 1986 and is in his second stint as union chief, has called on the union to break from its past of confrontation and infighting.
"We have to have mutual trust between the union and the management .... If labor relations deteriorate, both sides lose," he told Reuters.
In the 2013 election, Lee failed to secure a majority among Ulsan workers, winning 43 percent of the vote at the complex where more than half of Hyundai's Korean union members work, including many hardline faction leaders. Among non-factory workers such as salespeople and researchers he won 64 percent support.
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Park Tae-ju, a former adviser to Hyundai who wrote a book on its labour relations, said the current union leadership does not have sufficient support, especially on the shop floor, for a more cooperative stance with the company.
"Sometimes a labor union should make concessions to drive changes, such as boosting flexibility in production. But with a weak support base, the current leadership can't push ahead with such changes," Park said.
Union power has waned in South Korea in recent years, with few of the strikes and little of the violence that characterized industrial relations during the 1980s.
But the lingering threat of union action and ballooning labour costs have prompted other global carmakers to review their Korean operations, with General Motors set to pivot towards making India a new global manufacturing and export hub, taking some of the strain off its Korean base.
Critics sometimes portray Hyundai's union as "aristocratic" for its frequent strikes despite relatively high wages. Non-executive employees at Hyundai Motor in South Korea last year earned an average 97 million won ($88,725) in wages, overtime, bonuses and other benefits, according to a filing.
"Many factory workers seem to have nostalgia about hardline leaders ... but I think hardline leaders sometimes went too far," said one union member who works at Hyundai's research center on the outskirts of Seoul.