That complex history goes back to the 7th century. Feel free to ask me anything about it - I'm not an expert but I've spent the past year and a half learning Arabic language and learning both their and our own history here. I'll try to give you as balanced an answer as I can.

You are right - the conflict in Lebanon is related to the conflict in Gaza. That is because despite efforts to frame the conflict as "Israel against 2 million poor Palestinians" the real conflict is "2 billion Muslims against Israel". Every time we have a conflict with one of them, the others jump in to attack us. What's worse, they deliberately keep the Palestinians impoverished and suffering to fester conflict - they say this blatantly. The Palestinian cause is not about creating a state to care for the Palestinian people. The Palestinian cause is about creating an Islamic state to displace the Jewish state, and the Palestinian people are the tool to use to pressure the Jewish state and other interested states. They say this clearly - both the Palestinians and the other Arab nations. But that line is so different from Western line of thinking that I know you find it incredible. I implore you to simply read what they themselves say.