Morse is not a man of many fears. He's not a coward by any stretch of the imagination.
He is, however, afraid of dead bodies (necrophobia). Just looking at them makes him ill. He closes his eyes and looks away at every crime scene. A bit silly for a chief inspector, but there you go. He's not afraid of death in general (thanatophobia); it is just very inconvenient. It does keep him employed though.
Heights are another no go for Morse (acrophobia). Tall flights of stairs send his head into a tailspin. God forbid he should be on a roof. A simple, easily avoided fear; pop an antihistamine pill and he's right as rain.
He isn't afraid to be alone (monophobia). He is, however, afraid to be without someone, even if he never comes out and admits it. The Greeks, clever as they were, never found a word to describe the fear of losing a partner.
So Morse swallows down the rest of his beer and watches Lewis walk back to the bar with their empty glasses and selfishly hopes someone gets killed in Oxford soon enough. He asks for the life of a stranger so that his own isn't so lonesome.