Mr Lee travelled to Yangon after a summit in Beijing and is due to meet President Thein Sein. The trip was not made public ahead of time, as North Korea attempted to assassinate the South Korean president Chun Doo-hwan while visiting Myanmar in 1983 and tensions on the Korean peninsula are high following the North's botched rocket launch last month.
The democracy advocate Aung San Suu Kyi took her seat in parliament this month after spending 15 years under house arrest, affirming a political opening in a nation where only one person in 30 has a mobile phone.
The US lifted some economic and financial sanctions on Myanmar and Japan last month forgave about US$3.7 billion (Dh13.58) in debt.
"Korea corporate interest in Myanmar has grown since last year on optimism the US-led sanctions would be eased," said Kim Jong-sang, the director of the emerging market research team at the Korea Trade-Investment Promotion Agency in Seoul. "Cheap wages, which are a third of that in China, is one appealing factor."
Trade between the two countries amounted to $966 million in 2011, according to South Korean government statistics. Myanmar exported US$299 million worth of clothing, beans, marine products, jade and timber to South Korea and imported $667 million of South Korean motor vehicles, engines, spare parts, tin and steel products, and raw plastic materials.
North Korea may also be on the agenda when Mr Lee and Thein Sein meet. Hillary Clinton, the US secretary of state, in her visit in December expressed concern that Myanmar might be engaged in weapons trading with Kim Jong-un's regime. The US has blocked North Korean ships thought to be carrying arms to Myanmar.
Myanmar resumed diplomatic relations with the North in April 2007, having cut ties after the assassination attempt on Mr Chun that killed about 20 people, including the South Korean deputy prime minister and foreign minister.
The incident took place as Mr Chun was paying his respects at a mausoleum commemorating Ms Suu Kyi's father, Aung San.