The strategically located lake, about 4267 meters above sea level, stretches over an area stretching from the Indian territory Ladakh to Tibet, which is controlled by China, in the greater Kashmir region where India, China and Pakistan all claim territory.
The LAC, which indicates the de facto boundary, goes through the lake.
At least 20 Indian soldiers were killed in the incident. China has never acknowledged the victims of the clash.
In a joint statement, both parties agreed to strengthen communication on the ground to avoid misunderstandings or actions “that could complicate the situation.”
They also agreed not to act unilaterally which would change the situation on the ground, the statement said.
India and China share a 2,100-kilometer (3,379-kilometer) border in the Himalayas, but both sides claim on either side of it.
The LAC was formed in the aftermath of the Sino-Indian War in 1962 and appears on maps, but India and China do not agree on the exact location, often accusing the others of exceeding it or expanding their territory. .
In 1996, the two countries signed an agreement stating that neither party was allowed to fire within 2 kilometers (1.24 miles) of the LAC to prevent ‘dangerous military activities.
CNN’s James Griffiths and Helen Regan contributed to this report.