We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space X, the Lipschitz algebras Lipα(X) and lipα(X) are approximately biflat if and only if X is finite, provided that 0 < α < 1. We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.
