Sebastian is the twin brother of Viola, who has disguised herself as a man in order to protect herself from harm. She pretends that she is a man called Cesario. She is in the service of Duke Orsino and is ordered to serve as intermediary to win the heart of Olivia for the duke (Viola is however in love with Duke Orsino). When Cesario, whom she thought was dead in their shipwrecc, come to Illyria, he is mistaken for Cesario, the fake male persona Viola created for herself. In Greek mythology, Lethe was one of the five rivers of the underworld that Hades ruled. Greeks believed that when they dies and wanted to reincarnate they were required to drink the water of this river in order to forget all their previous life. In classic ancient Greek, the word lethe means forgetfulness or concealment which shows how the use of this river in this line of dialogue is highly eponymic since the play deals with a woman who conceals her own gender.
Sebastien knows that he is not dead but thinks he maybe has amnesia and that he might actuallly be Cesario and that he forgot it due to amnesia after the shipwreck. Therefore the corerct answer is C) Sebastian feels he may be suffering from amnesia after the shipwreck, and refers to the river Lethe, which is associated with forgetfulness in greek mythology.