Singer Jungkook's vehicle hit a taxi in Seoul on Saturday, and both he and the cab driver have since been treated for minor injuries, according to police in the capital.
The launches followed statements of displeasure by top North Korean officials over the slow pace of nuclear negotiations with the US.
Lee stepped out of a van to a throng of journalists and made a brief comment but did not answer questions about the accusation he gave bribes to influence former South Korean President Park Geun-hye.
The storm hit southern parts of the country on Wednesday night, prompting flood warnings and triggering landslides in affected areas.
The latest launch is seen by analysts as the most provocative test by North Korea since it started the talks with the United States in 2018.
The launch came hours after a senior North Korean diplomat announced that North Korea and the United States have agreed to resume working-level nuclear negotiations this weekend.
Bong Joon-ho's darkly comic tale of class war in the Seoul suburbs won the Palme D'or for best film at Cannes and is firming as an Oscar favourite next year, in what would be the first ever win for a Korean film.
Nearly 22,000 pigs have been culled since the outbreak was first confirmed last week in the border towns of Paju and Yeoncheon, but officials have yet to identify the infection route.
Typhoon Tapah earlier lashed parts of Japan's southern islands with heavy rain and strong winds that caused flooding and some minor injuries.
The launches came after North Korea said a day earlier that it was willing to restart nuclear talks with the United States in late September.
South Korea's Supreme Court also ordered a new trial for Samsung heir Lee Jae-yong, who was convicted of offences including bribery and embezzlement in connection with the scandal that brought down former president Park Geun-hye.
North Korean leader Kim Jong-un oversaw the test of a "super-large multiple rocket launcher", state news agency KCNA reports.
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