Sons and Lovers by D. H. Lawrence is a novel strongly influenced by the psychological theories of Sigmund Freud. The notion of "Oedipal" relationships in Lawrence relates only tangentially to the actual character of Oedipus in Sophocles' Oedipus Rex.
Oedipus himself was sent away from his home as an infant. When he kills Laius accidentally at the crossroads, he is not aware that Laius was his father. When he marries and has children by Jocasta, he does not know that Jocasta is his mother. Moreover, the marriage itself is not born from sexual longing, but rather is dynastic, a way of incorporating the hero who rids Thebes of the Sphinx into the ruling family of the city.
Freud, however, takes the basic plot elements of the Sophoclean drama to give a name to his notion of the Oedipus Complex, in which the male subconscious mind desires the mother sexually and thus sees the father as a rival and desires to kill him.
In Lawrence's novel, Paul Morel, the protagonist, exemplifies the Oedipus Complex by being so emotionally invested in his mother that he is unable to develop satisfactory sexual relationships with other women. He also resents and hates his overbearing father. After his mother's death, he is psychologically adrift, unable to resolve his primary Oedipal desires.