We study the Lipschitz property of a harmonic injective and sense-preserving mapping F of the unit disk D onto a bounded convex domain Omega in the complex plane C. In particular we show that F is bi-Lipschitz iff F is quasiconformal and Lipschitz. To this end we establish some auxiliary properties of harmonic mappings dealing with the boundary radial limiting values of the formal derivatives partial derivative F and partial derivative F.