We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).