My musing is that Oswald never asked for Mr. Abt, but asked for Mr. Abbott, an alias for David Atlee Phillips. This may have got him killed.
When Oswald was being moved for a lineup in the DPD headquarters he shouted out to the press that he wanted John Abt to represent him. That's how the press learned about it and tried to contact Abt.
Oswald: "I didn't shoot anyone. I want to get in touch with a lawyer, Mr. Abt, in New York City."
And according to Lou Nichols, head of the Dallas Bar Association, Oswald repeatedly asked for Abt to represent him.