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Under the right conditions on a compact metric space $X$ and on a Banachspace $E$, we give a description of the $2$-local (standard) isometries on theBanach space $\hbox{Lip}(X,E)$ of vector-valued Lipschitz functions from $X$ to$E$ in terms of a generalized composition operator, and we study when every$2$-local (standard) isometry on $\hbox{Lip}(X,E)$ is both linear andsurjective.

2-local standard isometries on vector-valued Lipschitz function spaces