The title works on two different levels; on an aural level, O'Neill makes it sound like the title refers to a positive rebirth and transformation. One could think of the image of "morning" becoming "electric"; this is an image of brightness and renewal. This is ironic given the title's actual meaning, but having it work on two levels adds surprising depth.
However, the "mourning" in the title is actually a reference to the clothing one wears at a funeral or when mourning the dead. The idea that funereal garb is "becoming" (i.e., attractive) is commentary on the character Lavinia (who is modeled after Electra in the Greek tragedy this play is based upon), a young woman who resents her mother's marriage to another man soon after the death of Lavinia's father. The idea that the attitude of mourning is "becoming" refers to Lavinia's character arc; she comes to realize she harbors too much anger and pain and it is not making her thrive.
Mourning Becomes Electra is a story styled after the Greek legend and the title refers to how the lead character is condemned to a life of mourning the disasters that befall her family. In the Greek legends, Electra is the sister to Orestes, and they are the children of Clytemnestra and Agamemnon. In the story, Clytemnestra and her lover Aegisthus kill Agamemnon in order to establish their relationship. Agamemnon is avenged by his children who murder both the mother and her lover but the story ends with Electra finding no peace in her life.
The Mannon family in the story by O’Neill goes through similar situations and the characters have a strong resemblance to the Greek legend. Electra is personified by Lavina, Clytemnestra is personified by Christine Mannon, Ezra (Agamemnon), Brant (Aegisthus), while Orin personifies Orestes. The Mannon family is marred by deaths, where Christine kills her husband (Ezra) to be with Brant, who is later killed by Orin. Christine commits suicide and so does Orin. The story ends with Lavina who goes back to their old lonely mansion.