Lee will leave on Sunday for a three-day trip to India, where he will meet Prime Minister Narendra Modi in New Delhi, National Security Adviser Wi Sung-lac told reporters.
The two leaders "are expected to reaffirm their mutual commitment to maintaining close coordination regarding energy supply chains amidst the turbulent international landscape", Wi said.
He added that the talks would seek to enhance cooperation in strategic sectors like shipbuilding, artificial intelligence and defence, and "lay the groundwork" for doubling two-way trade to $50 billion by 2030.
Lee and Modi will also discuss "continuing constructive cooperation for the sake of peace on the Korean Peninsula and within the region".
Lee will arrive in Hanoi later on Tuesday and meet with Vietnamese leader To Lam the following day, Wi said.
The pair will discuss "concrete measures to strengthen strategic and reciprocal cooperation amidst global uncertainties".
The talks will focus on energy security, supply chain stability, cooperation on critical minerals and other areas.
Vietnam is South Korea's third-largest trade partner, and the countries aim to hit $150 billion in annual goods and services volumes this decade.
Like many Asian economies, South Korea has faced mounting risks to its energy supplies since US-Israeli attacks on Iran in late February prompted Tehran to effectively close the crucial Strait of Hormuz.
Seoul said on Wednesday that it would procure more than 270 million barrels of crude oil via routes unaffected by the blockade of the strait, saying the move would help to stabilise domestic supply and demand.
Senior South Korean and Chinese officials will also hold economic talks next week aimed at ensuring a stable trade environment despite the shock from the war, the Yonhap news agency reported Thursday, citing Seoul's foreign ministry.
