Lee, a conservative who governed from 2008 to 2013, is the latest South Korean leader to be entangled in scandals or other problems after leaving office.
Pyongyang also wants to hold talks with the United States on denuclearisation and will suspend nuclear tests while those talks are under way, Seoul's envoy says on Tuesday, following a meeting with the North's leader Kim Jong-un.
Special envoys Suh Hoon and Chung Eui-yong will lead the Pyongyang visit but the upcoming military drills between US and South Korea could dampen their mission.
North Korean leader's sister Kim Yo-jong and the rest of the delegation departed for Pyongyang on Kim Jong-un's private jet on Sunday. A day before, she had offered a summit between two rival countries.
North Korean athletes will compete in figure skating, short track speed skating, Alpine skiing, cross-country skiing and hockey.
"All our weapons, including atomic bombs, hydrogen bombs and ballistic missiles are only aimed at the United States, not our brethren, nor China and Russia," Pyongyang's chief negotiator says.
Chinese President Xi Jinping and his visiting South Korean counterpart Moon Jae-in agreed in a meeting in Beijing they would cooperate in applying sanctions and pressure on North Korea.
The UN Security Council is expected to meet Wednesday, following Pyongyang's latest missile test. South Korea's military says the DPRK missile had an altitude of 4,500 kilometres and flew 960 kilometres over the sea between South Korea and Japan.
China, Pyongyang's sole ally, also rejects as "wrong" the latest US sanctions that also target Chinese companies doing business with the pariah state.
US President Donald Trump wants to counter the Pyongyang threat. During his meeting with military commanders he said "ultimately it will all work out."
South Korea's President Moon Jae-in and US President Donald Trump vow to increase pressure on Pyongyang to further isolate the country as US-ally Kuwait gives North Korea's ambassador a month to leave the Gulf state.
North Korea's state media marked the nation's founding anniversary with calls for a nuclear arms buildup, in defiance of mounting international sanctions.
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