Providing weapons to a state army (Lebanon) does not mean you're liable when another nation (Israel)starts killing its civilians. The only party which in your scenario might be guilty of war-crimes is the one doing the killing - not the one doing the defending.
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Russia says planned truce in Syria's Aleppo disrupted by Nusra Front attacks (Reuters)
from the article: Russia to gift Lebanon with arms, military supplies to bolster army