Here's what I know from a police source:
The two people Raymond Davis shot dead were returning from a court hearing where one of them was a witness in a murder case. One of the murder victims brother had been murdered a month ago and he was carrying a licensed pistol for his own protection, fearing for his own life. Raymond Davis, the US Consulate Technical Advisor, off-duty, comes out of a bank after withdrawing some money from an ATM machine. In a case of pure bad luck, the two guys on the motorcycle pass by his car as he drives away from the bank. At a traffic stop, Raymond sees the sidearm of one of the guys and pulls out his gun as a precuation thinking they either want to rob him or could be terrorists. In Lahore, people have a tendency to stare at foreigners because they are a novelty, especially in public. The guy on the motorcycle, who himself is paranoid about his own life, sees Raymond pull out his gun and grabs his own weapon for protection. He doesn't pull it out or fire at Raymond, just grabs it. At that moment Raymond, mistakenly thinking he's about to be fired upon and trained to pre-empt, fires shots through the windshield of his car at both the motorcycle guys killing both. They were shot from behind. He then takes pictures of the two dead people (to prove later that one of the dead guys was armed) and starts to leave the scene of the crime. At this moment eye-witnesses start to chase him. Raymond had already called for back up soon after the shots are fired. A back-up vehicle arrives in minutes and sees the traffic jam and takes the incoming lane on the wrong side to get to Raymond. In the process it hits two pedestrians, one of whom is killed. It then abandons the rescue plan and speeds away (i.e. hit and run). In the meantime a traffic warden and eyewitnesses stop Raymonds car, which is blocked by a traffic jam. He hit a rickshaw while trying to get away and overturns it with four children inside it. This further infuriates an already agitated crowd. Raymond refuses to come out of his car telling the traffic warden the crowd would kill him. A couple of angry people shatter his rear window and one of his back lights. The traffic warden, sensing the mood of the crowd and in a move that probably saved Raymond from being lynched by the crowd, asks Raymond to move into the passenger seat and himself gets into Raymonds driver seat and drives him to the nearest police station.