I think it goes to show that the ruling class of various countries have interests that align more with the ruling class of other countries, rather than with their own working-class citizens.
I hadn't really considered what you pointed out about the Lebanese government doing little to oppose the Israeli invasion, but it's an interesting point.
I think on the flip side, there are also examples of the ruling class sending their citizens off to die in wars that serve the interest of other ruling class factions that are completely at odds to the interests of those sent to die for them. WWI and WWII are obvious examples.
Another lesser-known example that comes to mind is of the White Army during the Russian Civil War. Many capitalist countries (including the US) sent contingents of soldiers to fight on the behalf of the capitalist interests of Russia attempting to pry back power from the Bolsheviks.
Of course, this was 'sold' to the Western public as 'preserving freedom and democracy' (as it always is), but in reality it was about trying to preserve the capitalist interests and power of a ruling class that had suffered defeat at the hands of the working class during the Russian Revolution.
The US contingent sent to join the White Army played a rather insignificant role in the conflict. One of the major issues was that most of the US soldiers actually sympathized with the soldiers and working class of the Red Army and despised the despotic, aristocratic leadership of the White Army and the various European monarchs and imperial interests they represented. Coming on the heels of WWI, few in the American working class were eager to become embroiled in yet another war in Europe in defense of imperial interests.
Due to their dissatisfaction of the White Army leadership they were placed under, and their fraternizing and sympathy to the Red Army, the US soldiers (and even many of their US officers) were not enthusiastic about engaging in hostilities with the Red Army. They were relegated to mostly-trivial, non-combat duties like securing/guarding goods and warehouses.
Eventually, US public opinion veered towards confusion and even anger about why young US men were - yet again - being sent to yet another war in defense of European capitalist and imperial interests. The US soldiers themselves were confused about the mission and why they were even there, and eventually President Wilson withdrew them.