For many of the millions of Taiwanese citizens who lined up at ballot booths on Saturday, the vote centered on the question of who should lead Taiwan in an increasingly tense standoff with its much larger, autocratic and heavily armed neighbor, China.

At the D.P.P.’s gathering outside its headquarters in Taipei, thousands of supporters, many of whom waved pink and green flags, cheered as Mr. Lai’s lead grew during the counting of the votes, which was displayed on a large screen on an outdoor stage.

In Chiayi, candidates from the three parties drove campaign vans around a large fountain at a circle in the city’s downtown, yelling slogans and urging people to vote.

The parade was festive, with candidate vans playing thumping club music, and several supporters dressed in inflatable dinosaur costumes for no apparent political reason.

Before Mr. Lai assumes the presidency in May, Taiwanese people — along with officials in Beijing and Washington — will be watching for any early signs of his approach to China, Taiwan’s biggest trading partner as well as a growing threat to its autonomy.

He has promised to stick with the approach of the current leader, President Tsai Ing-wen: keeping Beijing at arm’s length while seeking to avoid conflict, and strengthening ties with the United States and other democracies.

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