Where does the concept of "justice" originate? In duty as a citizen? In morality? In law? In the realm of the gods? What about in the duty of personal or familial allegiances? Electra addresses these questions, and in the process, teaches us that "justice" is a tricky concept. Too often, the notion of "justice" is used as justification for a questionable action (matricide, in this specific case). If an action is considered "wrong" in some ways but "right" in others, can the action still be considered to be just?
Electra is motivated not by justice, but by selfishness. She wants Aegisthus and her mother dead because they make her life miserable.
Electra is motivated only by justice.