I had never read the continuation of the Key to Time but apparently the writers have. I was searching the internet and came across 3 audio books that had been put to paper: The Judgement of Isskar, The Destroyer of Delights & The Chaos Pool. From these stories I gleaned more insight into the writers of Lost. Apparently they took elements of these stories along with the Key to Time and the Face of Evil took key plot lines shook them up and came up with Lost.
Excerpt from the Chaos Pool:
The Guardian asks Amy to hand over the segments, but the Doctor tells her to keep them safe. He points out that if the White Guardian gets the Key there will no longer be any disorder or free will in the Universe. He isn’t a Guardian of virtue, but a Guardian of control and domination, someone who follows the letter of the law but not the spirit of it. The White Guardian argues that chaos has no boundaries and says people can’t just make up the rules as they go along, but the Doctor says that having absolute certainty about everything is just another form of tyranny.
I’m not saying that everything matches 100 percent but you don’t have to be a genius to see that these events are similar and when put together with the mounting stack of other similarities that I have found you would have to be pretty gullible to believe that this is still a coincidence.
If you want to read the stories for yourself they can be found at the following locations:
The Judgement of Isskar:
The Destroyer of Delights:
The Chaos Pool: