Hello!
Let's go through this question, answer by answer, to determine why A is the best option:
Like Byron at Missolonghi, Jack London was slowly killed by the mistakes of the medical men who treated him.
A: Like Byron
This one is the best because it clearly shows that the writer is focusing on similarities between the two deaths without any unnecessary words.
B: Like Byron's death
Since we know that the sentence is talking about both men dying, it's not necessary to say it twice. It's slightly redundant.
C: Just as Byron died
Using this wording suggests that Byron died at the same time as Jack London, which isn't true.
D: Similar to Byron
This one might mislead readers into thinking the writer means that Byron and London are similar people, not that their deaths are similar.
E: As did Byron
This one isn't parallel, and makes it unclear what Byron "did" exactly. It would work if the second half of the sentence was written in active voice rather than passive: "As did Byron at Missolonghi, Jack London died because of mistakes made by the medical men who treated him." This makes it clearer that did is referring to the verb died.
I hope this helps! I'm available if you'd like any follow up.
