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 Doctor asks Amy if she trusts him and when she says she does, he tells her to let go of the Key. Then he tells Zara she has the choice of either surrendering the Key to the Grace or giving it to him. The Grace threaten to crush the Doctor, but he knows that they’ve manifested themselves inside the Key and they can’t leave it until everyone has let go. Zara asks Amy what she should do, but Amy insists that she makes the choice herself. Zara is angry that the Grace refuse to address her by her name, so she hands the Key to the Doctor, then he turns and jumps straight into the Chaos Pool. There’s a flash and everyone peers over the edge to see that the Pool has turned into a dark chasm full of jagged rocks. Moments later, the Doctor calls up to his friends and asks for their help getting him out.
The Doctor took a risk giving her the choice, but if he’d compelled her then he’d have been no better than the Grace. He risked everything on his faith that Zara was really a good person.
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: