Both are democracies, but both are also weak, unstable and violent.

Lebannon's central government lacks the power to disarm Hezbollah. Even if they had the power, they lack the will because they do NOT want to fight another civil war. Lebannon is also unstable at the moment, because the government is operating without Syrian control and with a massive armed militia camped in the Bekka valley. Lebannon is violent: not only are there continued assassinations against political leaders unpopular to Syria but Hezbollah has conducted a continuous series of rocket attacks and cross border raids.

Israel is weak in terms of geography (no strategic depth), small population, political will (no prolonged wars, casualty sensitive, sensitive to press/popular opinion) and intelligence capability. Israel's political system has always been notoriously unstable - few governments last more than a couple of years. The fact that Israeli politics is populated by the same returning cast of characters each election cycle simply means that the swings in policy with each election are more pronounced. Israel is famously willing to fight and will use collective punishment, retaliation and assassination to accomplish its ends.

Is it any wonder they come into conflict?