Mt. Kailash as we refer to it in the present day is the Mount Meru of yesteryear. It is in the region around Mt. Kailash that Pacceka Buddhas will reside at a time just before a Supreme Buddha is born to this world. That is when the eminent coming of a Supreme Buddha is talked about amongst the general population of that time.
So Mt. Kailash is a very storied mountain, the equally storied lake and the storied flower in it. Mt. Kailash is the mythical Mt. Meru. Read about it in the "Saptha Suryodgamana Sutta" The Sermon of the Seven Suns (Anguttara Nikaya VII. 62). In it the Buddha explains in detail about the events that would unfold, and in it, this monarch of mountains will get consumed and burnt, that neither ashes not soot will remain.
The Lake Anavatapta is said to be so sheltered and covered that the direct rays from the sun would not fall and the lake would not dry up until the day this world would come to an end, as per the Saptha Suryodgamana Sutta. In this "Sermon of the Seven Suns" the Supreme Buddha, tells us about the end of the earth due to the expansion of the dying sun.
In the Manual of Buddhism by Spence Hardy he has this to say about Mt. Kailash & the Lake Anavatapta - in page 42:
"The great forest is in the northern part of Jambudwipa, which, from the southern extremity, gradually increases in height, until it attains an elevation of 500 yojanas, in the mountains of Gandhamadana, Kailasa, Chitrakuta, and others, there being in all 84,000.. These mountains are inhabited by an infinite number of dewas and yakas, and are beautified by 500 rivers, filled with the most delicious water, and by the seven great lakes, among which is the Anotatta-wila. This lake is 800 miles long, and as many broad and deep; and there are four places in it in which the Budhas, Pase-Budhas, rahats, and rishis are accustomed to bathe; and six other places where the dewas from the six inferior heavens bathe.
..... On the four sides of Anotatta are four mouths or doors, whence proceed as many rivers; they are, the lion-mouth, the elephant, the horse, and the bull. The banks of these rivers abound with the animals from which they take their name. The rivers that pass to the north-east and west flow three times round the lake without touching each other, and after passing through countries not inhabited by man, fall into the sea. The river that runs to the south also passes three times round the lake, then rushes from the midst of a rock, and flows in a straight line 60 yojanas.. It then strikes against another rock, and rises into the sky, like a mount of gems 12 miles in size, flows through the sky for the space of 60 jojanas, and strikes against the rock Tiyaggala. This rock it has broken by its immense force; and after this it violently rushes on a further space of 60 yojanas, after which it flows on an inclined plane, strikes and breaks the ponderous Pansu-parwata or Five Mountains, and again passes on 60
yojanas. It then flows 60 yojanas further, through a cave, strikes the four-sided rock Wijja, and is lastly divided into five streams, like five fingers, that are the five great livers (Ganga, Yumuna, Acirawati, Sarabhu, and Mahi), which, after watering Jambudwipa, fall into the sea."
The five great rivers of India: the Ganga, the Yamuna, the Aciravati, the Sarabhu, and the Mahi, is said to have its beginning in Lake Anavatapta & around Mt. Meru.
