No He is also "PO Lazarus" not the Biblical Lazarus, the Lazarus of the chain gang song. Like many peoples who have had their own beliefs stripped and replaced with the beliefs of their oppressors the displaced Africans Altered the Biblical Lazarus to fit their own needs. Biblical Lazarus gets no rest walking the earth for all eternally, Chain gang song Lazarus gets no peace from the High Sherriff's(Authority) dogged pursuit.
Ulysses gets home in the end of the movie, But,Lazarus is still out on the road eluding the High Sherriff. Lazarus will remain out there at least until Ulysses acknowledges his spiritual side which is tied up in Lazarus. Thus the title "Oh Brother, Where art Thou?"
Ulysses also represents man desire for Society he is after all a Hero of the Advanced civilization of ancient Greece . Lazarus on the other hand represents man at odds with society. Another example of the paradox in the character is that Ulysses was thrown in jail for practicing law without a license And almost hung by the High sherriff because as the High sherriff informs him "Law is man's domain".