This is an interesting question because by adding 'la' the whole sentence structure changes. See how this sentence is parsed when 'la' is absent:
(i) Fue una ridícula secuencia de hechos que me llevó al borde de la muerte.
The DO is a Noun Phrase (sintagma nominal in Spanish), where "secuencia" is the núcleo, and "que me llevó al borde de la muerte" is a complement of that núcleo (what we call in Spanish a complemento de nombre).
Now see how it's parsed when 'la' is present:
(ii) Fue una ridícula secuencia de hechos la que me llevó al borde de la muerte.
Here, the subject is a NP, whose original núcleo ("secuencia") has been elided to avoid repetition. The complete NP would be "la [secuencia] que me llevó al borde de la muerte".
So by adding the 'la' a different part of the sentence becomes the subject. In sentence (i), the subject is omitted. That would only make sense if there was a sequence of events already mentioned before, so the reader would be able to know what sequence the writer is talking about. Since in the book that sentence is at the beginning of a paragraph, the reader would be really puzzled as to what sequence the writer is talking about –that misterious sequence that would be the omitted subject.
In sentence (ii), on the other hand, the subject is "la [secuencia] que me llevó al borde de la muerte". Here you have a noun ("secuencia"), with a determiner ("la") and a complemento to that noun ("que me llevó al borde de la muerte"). Now that should be enough to identify what sequence the writer is talking about. With this last sentence, the reader has no concerns, he/she isn't puzzled and wondering what the heck the writer is talking about (which is a good thing when reading a book).
But this gets even more complex when the second part ("y una secuencia aún más ridícula la que propició que sobreviviera") is added. This one is harder to parse since it's not even a sentence, for it lacks a verb. The complete sentence would be:
(iii) Y [fue] una secuencia aún más ridícula que propició que sobreviviera.
Or...
(iv) Y [fue] una secuencia aún más ridícula la que propició que sobreviviera.
In sentence (iii), the omitted subject (see parsing of sentence i) is the same as the one in the first part. But by saying "una ridícula secuencia" and "una secuencia aún más ridícula" you are saying they are different sequences. That is, how could something be "ridiculous" and "even more ridiculous" at the same time? By being more ridiculous than itself? As you can see, that interpretation doesn't hold water.
Now, by looking at sentence (iv), the subject is now "la [secuencia] que propició que sobreviviera" (see parsing of sentence ii). This subject is evidently different from the subject in the first part ("la secuencia que me llevó al borde de la muerte" vs "la secuencia que propició que sobreviviera"), so that makes it perfectly sensical that one is only "ridiculous" while the second is "even more ridiculous". I hope you can see now why 'la' is not only less puzzling, but strictly necessary there for the whole sentence to make sense.
This may seem a little bit too complex a parsing for readers to do it "on the go", but this is what any Spanish speaker does even without noticing they are doing it (and even those who can't parse). They may not be able to tell you what's not working there, but they will surely tell there's something wrong to it.
Concerning the subjunctive thing, that is harder to tell. All I can say is that "sobrevivía" is definitely not right. Imperfect Preterite (sobrevivía) is generally used for actions that last in time. You can't be surviving, you either survive or not. In any case, the question should be: why not "sobreviví" instead of "sobreviviera"? But sobreviví doesn't work either, you must use a subjunctive. The reason for using a subjunctive is that the author says that the "ridiculous sequence" is what would allow the protagonist to survive. It looks ahead to the future while the action is in the past (from here).
