"Taiwanese people are people of the world; Taiwanese people have the right to engage with the world," Lai told reporters at Taipei's international airport after his flight on the Eswatini king's plane.
Lai flew on the king's plane to Eswatini on Saturday.
His original trip scheduled for April 22 to 26 to attend the 40th anniversary of King Mswati III's accession and his 58th birthday was postponed after Seychelles, Mauritius and Madagascar revoked overflight permits following "intense pressure" from China, a senior aide said previously.
China claims Taiwan is part of its territory and opposes the self-governed island's participation in international organisations and exchanges with other countries.
The United States slammed China's "intimidation campaign" after Lai's first trip was delayed. The remarks were rejected by China's foreign minister as "baseless accusations."