I think it's quite dangerous to point at individual crimes and apply them as some indication of the overall situation. This should never have happened, no question. But that doesn't mean it happens often. Shit things happen everywhere. I'd like to see data before I make any sweeping judgements about Lebanese or Arabic (!) culture.
If I remember right, honor killings are mostly confined to the rural, backwater, tribal areas, which is were people can be a bit more backwards and crazy. (Trust me, I have experience) The tradition also predates Islam and was practiced by tribes for quite a while before Islam even existed.
I've also heard that honor killings happen in India, which is primarily Hindu. Somehow, I wouldn't be too shocked if someone pulled shit like that here where I live in the US.