In this paper left ϕ-biflatness of abstract Segal algebras is investigated. For a locally compact group G, we show that any abstract Segal algebra with respect to L 1 (G) is left ϕ-biflat if and only if the underlying group G is amenable. We then prove that the Lipschitz algebras Lip α (X) and lip α (X) are left C-ϕ-biflat if and only if X is finite. Finally, we also study left ϕ-biflatness of lower triangular matrix algebras.