I disagree. If I did agree, I certainly wouldn't look at my feet or at the ceiling. I'd keep my eye on the lion! (Para. 11)
Meaning: I don't agree that entering a room full of people is like going into a lion's cage. Suppose I agreed with such a thought, I would not look at my feet or at the ceiling but look carefully at the lion to make sure it would not kill me because the lion was most dangerous.
Notice the emphatic use of "did" in "If I did agree...". Here are some more examples of the use of "did" for added stress.
He did tell me about it. 他的确告诉了我这事儿。
In the present tense, "do" or "does" is used:
I do feel sorry for him. 我确实为他感到遗憾。
A little knowledge does seem to be a dangerous thing. 看来一知半解确实是件危险的事。
Also in the sentence, please note the use of the "if clause" to talk about unreal situations. For example,
If he started it now, he would not finish it in time. 就算他现在开始做,也不可能按时完成这项工作了。
If you had asked, I would have told you. 如果你当时问了，我会告诉你的。