The strategically located lake, 14,000 feet (4,267 meters) above sea level, stretches from the Indian province of Ladakh to China’s Tibet, in the greater Kashmir region where India, China and Pakistan claim the territories.
The LAC, which is the actual border, passes through the lake.
And killed at least 20 Indian soldiers in that accident. China has never admitted casualties from this clash.
In a joint statement, the two sides agreed to strengthen contact on the ground to avoid misunderstanding or take action that “may complicate the situation.”
The statement added that they also agreed not to take any unilateral action that would change the situation on the ground.
India and China share a 2,100-mile (3,379 km) border in the Himalayas, but both sides claim territories on either side of it.
The LAC was created in the aftermath of the Sino-Indian War in 1962 and appeared on maps, but India and China do not agree on its exact location and accuse the other of regularly of overreaching or seeking to expand their territories.
In 1996, the two countries signed an agreement stipulating that neither side would fire within 2 kilometers (1.24 miles) of the Latin America and the Caribbean region “to prevent dangerous military activities”.
James Griffiths of CNN and Helen Reagan contributed to this report.