To anybody giving Luke a hard time for abandoning the group, remember this:
Luke is only armed with a machete when the incident with the wind turbine kicks off. To take on Carver and his men who are all carrying guns, it would be suicide. This isn’t The Last Of Us, he can’t just throw bottles or bricks to draw them away one by one and pick them off. Maybe any other time a trick like that might work, but Carver is literally threatening to kill his hostages and waiting for them to give themselves up.
Also depending if you asked Kenny about Luke’s whereabouts, the man says that he told Luke to take a hike after he was ‘whining’ about something. If this was before or after the hostage situation is unclear, as is what exactly Luke was whining about. But if one thing to take note of is that if Clementine says they should go look for Luke rather than take out one of Carver’s men, Kenny looks annoyed and shoots the man dead anyway. In fact any mention of Luke irritates Kenny.
Even in the way that he shoots the guy, if you picked “maybe we should find Luke” Kenny actually smiles afterwards in a very 'look at me I'm awesome, we don't need that dickhead's help'. Plus Luke whining and running off without a good reason is out of character as it is, which is why I don’t think Kenny has told Clementine everything, or the real reason Luke is gone.
Why is Kenny acting his way? I think it is perhaps because Kenny is worried of Clementine being taken away again, and it has got him defensive. He probably feels like it’s his right to take her under his wing after what they and Lee went through, and for that be threatened by this new group…well, we know from experience how Kenny can be. That, and how Duck’s name slipped when addressing Clem, he probably feels that if she’s there like a daughter along with his new girlfriend, he can finally get his life back together after losing Kat and Duck. So getting Luke or anything out of the picture that threatens that, might be a plus for him.
But even Luke was there and turned himself in to Carver, it would also be suicide. From what was mentioned, Luke was the one that got the group to leave Carver in the first place. Being the leader the caused that, Carver wouldn’t take any chances with Luke, he would kill him.
One more thing to remember as well [as I saw someone mention in a post previously] is that Carlos took Luke to one side after the bridge incident to speak alone with him in private. No doubt they would’ve spoken about Nick and killing a man, but it is also a possibility they may have talked about a back up plan in the event Carver found them. And being Luke is the most capable man of the group [not having to worry about the heavily pregnant Rebecca’s well being like Alvin, is or being emotionally unstable as Nick] he would be the best person to rely if anything went wrong.
Do I believe Luke has run off like coward? No. I think he is still around somewhere keeping an eye on them from a distance. If he does intend to help them, the best Luke can do at the moment is keep out of sight. Even if he managed to get a gun, Carver might wind up still doing the whole ‘threaten to kill a hostage’ thing again like with Kenny and wouldn’t help anybody.
And darn it people this is Luke, not Ben. He isn’t a coward and he wouldn’t abandon people like a pussy.