Lee could have come from Tenth on Crawford to Jefferson since there was a School on Tenth here. The head in parking along the street was there in 1963 which would make it even harder to spot a person walking down the sidewalk. You can see that the sidewalk isn't strait nor a clearview to any patrol car that would have been going down the street.
Word of Officer Tippitts shooting was already out on the police radios so there were more and more police cars in the area looking for that shooter.