Lake Titicaca sits at nearly four thousand metres on the border of Peru and Bolivia, and Andean tradition places the origin of the world's order there.
In the Inca account recorded by colonial chroniclers, the creator brought the sun, moon and stars out of the lake or from the Island of the Sun within it, and sent the first Inca and his sister northward from there to found Cusco, carrying a golden rod that would sink into the ground where they were to settle. Versions differ in detail between the chroniclers, which is itself informative: Betanzos, Cobo and Garcilaso de la Vega were recording material from different informants at different removes, and the Inca state had reasons to standardise an origin story that grounded its dynasty in the most sacred lake in the region.
The Island of the Sun carried a major shrine complex, with a sacred rock, a temple and accommodation for pilgrims who came from across the empire, and the pilgrimage was managed as a state undertaking with progressive stages of purification along the route.
The lake was there long before the Inca, and so was its sanctity. The Inca claim on it is best read as the annexation of an existing sacred centre by a state that needed one, which is a pattern their administration repeated across the Andes, incorporating regional shrines and their staff into an imperial system rather than suppressing them.