The existence of a great lake within the Kalahari was known to Europeans from early reports of Bekwena and Batawana people, though it wasn't reached by them until the mid-19th century. Livingstone arrived on August 1 1849, with Cotton, Oswell and Murray, narrowly beating Charles Andersson, who set out specifically to reach it from present-day Namibia.
In his book, entitled Lake Ngami
Andersson was hugely disappointed with what he first took to be Lake Ngami. He wrote:At last a blue line of great extent appeared in the distance, and I made sure it was the long-sought object; but I was still doomed in my disappointment. It turned out to be merely a large hollow in the rainy season filled with water, but now dry and covered with saline encrustations.
However, he hadn't reached the lake at this stage, and after getting beyond some pans and reed beds, and over a series of sand ridges, he finally glimpsed the water, and described the moment:
There, indeed, at no very great distance, lay spread before me an immense sheet of water bounded only by the horizon – the object of my ambition for years, and for which I have abandoned home and friends, and risked my life.
Visiting the lake is certainly easier than it was for those first explorers, though it's by no means well signposted, and at times it can still be very disappointing. Note that although very large when full, a high rate of evaporation and a very shallow profile means that the area covered by water can vary enormously.