What was Laius doing when he was killed in Oedipus Rex?
Laius and Jocasta were both warned by the Oracle at Delphi (consulting Apollo) that their child would one day grow up, kill his father, and marry his mother. In order to escape this fate, Laius and Jocasta bind the ankles of their son when he is but a baby, and abandon him on top of a mountain. The baby, Oedipus, is saved and brought to the king and queen of Corinth who raise him as their own.
Many years later, the teenaged Oedipus hears of his original fate, and leaves his home in anger, an attempt to avoid the tragedy. At the same time, Laius has received omens that his son might return to kill him. Therefore, he is traveling to consult the Oracle at Delphi concerning these omens. On this journey he happens to run into Oedipus at a crossroads. Both father and son likely display a similar attitude of anger and arrogance. Neither will yield to the other and, as the story goes, Oedipus kills Laius, securing his original fate in a remarkably ironic moment of running in to one another.