This discussion may contain spoilers!
... be a traitor is if he devised a plan with Carver. Sounds weird, right? Actually, no. Clem, Pete, and Nick were all gone for a whole day. For all we know, this was the perfect opportunity for Luke to set up a scheme that everyone would fall for...
Before I begin, this is NOT my main theory. I made another topic on my main theory. However, there is one thing that leads me to believe that this is a second possible scenario: Carver going to the house alone. On what planet does it make sense to go alone to a house, possibly filled with people, alone and only having a small handgun? He would be crazy if he thinks he can convince them to go back. Heck, he would be crazy if he expects to walk out alive. Unless he knew who was supposed to be there...
During that whole day timespan, Luke might have bumped into Carver. Knowing Carver would threaten or kill him, he was forced to listen to his demands. Quite likely, Carver demanded that he surrender Rebecca and no one else would get hurt. Having no choice, he agrees. With three people out of the picture and in the woods somewhere, all he needs to remove is Alvin. He would never agree to this, so he tells him to go along and find the others. With that, only Carlos and Sarah are in Carver's way... Or not.
Carlos is a doctor so it would be best if he stayed for Sarah's sake and if someone might've came back. He can also fight off intruders if he must. However, what if Carver was to appear and use Sarah as a hostage? Carlos would surrender instantly. Rebecca would be able to leave with Carver and no one would be hurt. Now why didn't this happen? Because an unexpected person came back... Alone.
Clem ruined the plan. By coming back, Carlos and Rebecca were able to find out what had happened. Knowing this is a serious situation, they had no choice but to leave to find the others, having Clem safeguard the house with Sarah just in case. When Carver came back, expecting to see Carlos, Sarah, and Rebecca, he only finds a girl who he did not recognize. After finding no one in the house, he expected that Luke might have betrayed him and planned to kill him. This is where everything adds up.
Luke comes back with everyone and finds out that Carver arrives at the house already. Knowing that he might be targeted for unknowingly betraying the agreement, he runs off with the group. Luke is trying to run away as far north as possible, while looking for survivors to help fight against Carver in the process. Little did he know they came fully armed and prepared. Realizing that they were caught, he runs away from the group, hoping to go back to Carvers camp before they do and help them secretly from the inside with support of anti Carver followers. This paragraph is least likely, and that is why I made this my second possible outcome. One thing I can guarantee though is Kenny did NOT kill Luke.
First off, Luke was with Nick last. We know this when he tells Nick to go get a drink. Nick left to see what was going on with Walter and Clem, probably under Luke's order. This was the perfect opportunity for him to run off. However, the windmill was kicking in and it had to be shut down. Kenny was the one who asked for it to be shut down, confirming Luke was still alive at this time. Kenn would need a sound to be a distraction while he shoots Luke. They don't have a silencer and a gunshot can be heard for miles. Not long after, a walker attack occurs. No one in their right mind, insane or not, would kill a human, wasting a bullet in the process, when they can use it to attack the walker while also having another human to help in the process. This was the only other opportunity to kill Luke and that too is unlikely. When Carver captures the group, this is when Luke runs off, realizing that this is his best chance. Kenny must have been with him so he needed to piss Kenny off in order for him to be fine with Luke leaving. And there we have it.
I call this scenario 2 because it has more speculations than fact. The key piece of evidence is Carver going alone, but otherwise this whole assumption can be thrown to the trash. One thing for sure, Kenny did not, could not, and would not kill Luke at any possible time.