Self-ruled Taiwan faces the constant threat of invasion from China, which claims the island as part of its territory and has refused to renounce the use of force to bring it under its control.
Washington has long been Taipei's most important backer and biggest supplier of arms but Trump's transactional style of diplomacy has raised concerns about his willingness to defend the island.
"Taiwan must be prepared for danger in times of peace, continue to increase its defence budget, strengthen its defence capabilities, and demonstrate its determination to protect the country," Lai said in a speech delivered in front of reporters at the Presidential Office Building.
While Taiwan regards itself as a sovereign nation, most countries, including the United States, have severed official diplomatic ties with the island in favour of Beijing.
But many governments maintain close, unofficial relations with Taipei, which has become a powerhouse in the semiconductor industry.
Trump rattled nerves during his election campaign by suggesting Taiwan should pay the United States for protection and accusing the island of stealing the US chip industry.
While Taipei has increased spending on its military in recent years, the island of 23 million people still relies heavily on US arms sales as a deterrence against Beijing.
Lai has sought to get on side with the incoming US administration and show the island's commitment to investing more in its own defence.
But he is struggling to push his government's budget, which includes record defence spending, through parliament, which is controlled by opposition parties.
Lai said in Wednesday's speech "protecting Taiwan's democracy and security is everyone's responsibility".
"We must pool every ounce of our strength to improve our whole-of-society defence resilience, build capabilities that can respond to large-scale disasters and deter threats and invasions," he said.
Chinese President Xi Jinping said in a New Year's address on Tuesday that "no one can stop" unification with Taiwan.
"Chinese people on both sides of the Taiwan Strait are one family. No one can sever our blood ties, and no one can stop the historical trend of the reunification of the motherland," Xi said in a speech broadcast on state media.
China has intensified pressure on Taiwan in recent years and has staged three rounds of major military drills since Lai came to power in May.
The dispute between China and Taiwan dates back to 1949 when Chiang Kai-shek's nationalist forces fled to the island after losing a civil war with Mao Zedong's communist fighters.
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