Pictures of Sangay and other Tibetan monks at Pangong Tso were posted on the official website of the Central Tibetan Administration.
New Delhi's decision could potentially trigger another sore point between the two nations. China calls the 82-year-old Dalai Lama, who has been living in India since 1959, a dangerous separatist and opposes his presence in India.
In recent months, Beijing's criticism of India on issues related to the Dalai Lama has sharpened. China strongly opposed his visit to Tawang in Arunachal Pradesh in India's northeast in April. China does not recognize Arunachal Pradesh as a part of India and claims it as Chinese territory.
The LAC passes through Pangong Tso, although China and India have differences on the alignment of the imaginary line. India accuses China of illegal partial occupation of the lake, which has Tibet on its eastern end.
The standoff at the tri-junction has now been going on for over three weeks. Despite that, Chinese President Xi Jinping and Indian Prime Minister Narendra Modi met during an informal meeting of BRICS leaders on the sidelines of the G20 Summit in Hamburg, Germany on Friday.
Dr. Deep Kisor Datta-Ray, Associate Professor, at the New Delhi-based O.P. Jindal University and the author of The Making of Indian Diplomacy: A critique of Eurocentrism, told Sputnik that India should avoid tactics that can boomerang when dealing with China.
"India's use of religion and superstition for politics will seem quaint to Beijing which officially reposes its faith in science and outclasses New Delhi in wealth and power. India's tactics expose our weakness. New Delhi cannot challenge Beijing in any meaningful way, and so relies on these 'cultural' symbols which lack any material substance that can deter China in any manner," Dr. Datta-Ray said.