[impossiblefork]

An invasion can be legal when authorized by the UNSC due to some crisis or when it's done in self-defence or to defend some other country.

So examples of some illegal invasions: US invasion of Iraq, Russian invasion of Ukraine. Legal invasions (although illegalities were found afterwards, but much of the invasion was legal) are the invasion of Libya, probably the NATO invasion of Serbia depending on what actually happened (there are still some open questions-- it matters why people went in).

Reasons to think the Israeli invasion of Lebanon is illegal are the mass-bulldosing of civilian buildings, destruction of farmland, some opinion articles about Lebanese territory being legitimately Israeli territory and an appropriate target for settlement etc. It shows a plan that is not primarily about self-defence.