In November 1987, nine months before the Summer Games in Seoul, North Korean agents detonated a bomb on Korean Air Flight 858, killing all 104 passengers and 11 crew.
But speaking to South Korean businessmen in Athens, Lee pointed out that the 1988 Games were the most participated-in Olympics held up to that point.
During the 2002 World Cup, North Korean patrol boats crossed the disputed maritime border and exchanged fire with South Korean vessels, killing six sailors as South Korea prepared to play Turkey in a playoff for third place.
Lee said the tournament was one of the most successful World Cups ever held.
"The Pyeongchang Olympics will also be a success," he added, in quotes carried by Yonhap News Agency on Monday.
Lee also described the Games as an opportunity for North Korean leader Kim Jong Un to send a message to the world that the nuclear-armed nation was in favour of peace.
"(It) will be a good opportunity for the North Korean leader to send a message that 'what we want is not anxiety but we also want peace,'" Lee said. "He may think whatever he wants to think, but if I were him, I would think that way."
There is no word yet on whether North Korean athletes will participate in the Games in the mountainous resort town of Pyeongchang, just 80km from the heavily fortified border with North Korea, but Lee said the signs were "positive".
"There have been a few positive signs (regarding the North's participation), but we're not yet at the point where we can disclose them," he added.
Tensions on the Korean peninsula have risen in recent months as Kim Jong Un and U.S. President Donald Trump exchanged threats and insults over the North's nuclear and missile development programme.
France's Sports Minister Laura Flessel said last month that if the crisis in the region deepened and athletes' security could not be guaranteed then they would not travel to the Games.
Members of France's Winter Olympics team, however, have remained optimistic the country will not boycott.
South Korea has been taking extra measures to try to ensure the safety of the 2018 Winter Games, including setting up a crack cyber defence team and doubling the number of troops, according to officials and documents reviewed by Reuters.
(Writing by Simon Jennings in Bengaluru, editing by Ed Osmond)
