The sentence that is correctly puntuated is "This article argues that there are some interesting similarities between Lincoln's and Kennedy's assassinations. " Option A is correct.
The possessive 's shows that something belongs to someone or something.
According to the rule, we use ’s after a singular noun and ’ after a plural noun. In this case, both names Lincoln and Kennedy do not end in S, so, in order to show that something belongs to them, we have to add 's.