It is believed that, first, the lake was created when the Sun God filled the area with tears after pumas ate his children.
"Legends of the Aymara Indians say that the Creator God Viracocha rose from Lake Titicaca during the time of darkness to bring forth light. Viracocha was a storm god and a sun god who was represented as wearing the sun for a crown, with thunderbolts in his hands, and tears descending from his eyes as rain. He wandered the earth disguised as a beggar and wept when he saw the plight of the creatures he had created, but knew that he must sustain them. Viracocha made the earth, the stars, the sky and mankind, but his first creation displeased him, so he destroyed it with a flood and made a new, better one, taking to his wanderings as a beggar, teaching his new creations the rudiments of civilization, as well as working numerous miracles. Viracocha eventually disappeared across the Pacific Ocean (by walking on the water), setting off near Manta Ecuador, and never returned. It was thought that Viracocha would re-appear in times of trouble. References are also found of a group of men named the suncasapa or bearded ones - they were the mythic soldiers of Viracocha, aka the 'angelic warriors of Viracocha'." —Source: Pre-Inca Civilization http://www.crystalinks.com/preinca.html