is it possible to travel from lebanon to israel?

I know there is a lot of fuss going on in the Middle East area, but I maybe have to go to Lebanon. I am not quite sure, but I know that I am not willing to risk my life there. I am fascinated with East in general even some things are just insane. I liked Israel for quite some time if I exclude the war events but wish to see Jerusalem and this holy land. To cut the long story, if I would like to visit Israel is that possible to be done from Lebanon?

One is for sure if you are going other way around, meaning going from Israel to Lebanon that wont happen, not being allowed. Usually people are for these kinds of transitions using two different passports. I am not sure if that is a safe place right now, traveling to this area is not recommendable as far as I know, specially combining these two countries.