Trump and Lee are meeting privately at the Istana, the prime minister's office and residence, for one-on-one talks before attending a working lunch with senior aides.
Lee met earlier on Sunday with Kim to discuss regional developments and wish the North Korean success in his highly anticipated summit with Trump.
Trump and Kim will meet on Tuesday at 9 a.m. local time (01:00 GMT) for talks on denuclearization. The summit was made possible after a significant thaw in tensions on the Korean Peninsula.
The US-North Korean summit will mark the first-ever meeting of sitting leaders of the two countries.