Correct this: The virus may cause AIDS, cancer, or even kill.

Question

Do I need to add a word in front of cancer? Would this be correct?

The virus may cause AIDS, produce cancer, or even kill.

Answer 1

No. Take a good look at those three parts of the series:

cause AIDS (verb + direct object)
produce cancer (erb + direct object)
even kill (adverb + verb)

Do you see that they are not the same? That they are not parallel?

Go back to the original sentence and take the series apart as I did in your sentence. What do you find?

Answer 2

The virus may cause AIDS, produce cancer, or kill people.

This makes all three have a verb + direct object.