We study approximate biflatness and Johnson pseudo-contractibility of Lipschitz algebras. We show that for a compact metric space $X,$ the Lipschitz algebras $Lip_{\alpha}(X)$ and $\ell ip_{\alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha<1$. Also enough and sufficient condition for vector-valued Lipschitz algebras to be Johnson pseudo-contractible is given. We also show that some triangular Banach algebras are not approximately biflat.
