There's not much known about the actual tournament itself, but there are references to it in comics. Another source you'd be interested in is the show Mortal Kombat Conquest, it was a show about the original Kung Lao and his adventures. They had some original characters that were allies to him.
Another cool reference to what life was like 500 years prior was the Mortal Kombat novel by Jeff Rovin. In the prologue they describe a young Kung Lao before he even began training to be the legend he would eventually become, they described Shang Tsung as being loosely related to Kung Lao by marrying one of his aunts but would experiment with his sorcery in the forest and he abandoned his family when he discovered a way into Outworld.
I honestly just think that the Great Kung Lao is a plot device to set up the stakes of the current tournament. You don't really need to know about the history of him. You just need to know that he saved the world once, became the champion and in his lifetime he formed the White Lotus society under the order of light. You also need to know that it was Goro who was the one to end his life, this gives Goro some sort of menace and pits him as the biggest threat to the heroes in the first game and 10th tournament. This is something the writers of that Mortal Kombat movie should have considered before using him in their movie because that Goro was absolute TRASH.
