The border with Lebanon, Syria, and Jordan consist of multiple fences marking, among other things, the International Border and a buffer/security zone. The buffer zone is Israeli territory set up for security. This particular fence MAY be the fence marking the beginning of the security buffer and not Lebanese territory. So, before spouting immediate, blind hatred towards Israel, try and educate yourself.
U.S. to defend Syrian rebels with airpower, including from Assad (Reuters)
from the article: 3 Lebanese soldiers, journalist killed in clash on Israel-Lebanon border