$Pi{n}^c$ and Lipschitz structures on products of manifolds

The topological condition for the existence of a $pi{n}^c$ structure on the product of two Riemannian manifolds is derived and applied to construct examples of manifolds having the weaker Lipschitz structure, but no $pi{n}^c$ structure. An example of a five-dimensional manifold with this property is given; it is pointed out that there are no manifolds of lower dimension with this property.