I do not think that you should use "the" at all in this context. I cannot give a grammatical reason, but would say that in this sense a second time does not yet exist, so you cannot refer to it using a definite article. With that in mind, "I'd like to read this novel a second time" sounds better to me. I would say "I'd like to read this novel again."
Once you have read the novel again, you could say "The second time I read the novel, I noticed a lot more details", as suggested by Monika.
Examples of using "for":
Teacher to student: "For the second time (of asking), behave yourself."
Wife to husband: "(For) the first time we go on holiday together, can we book a first-class seat?" [For is optional and possibly a little unnatural]
Book reader: ""(For) the second time I read this novel, I want to try it in a foreign language." [Again, for is optional]