In Paper I of this series, we presented a new N-body light-cone simulation from the MICE Collaboration, the MICE Grand Challenge (MICE-GC), containing about 70 billion dark-matter particles in a (3 h −1 Gpc)3 comoving volume, from which we built halo and galaxy catalogues using a Halo Occupation Distribution and Halo Abundance Matching technique, as presented in the companion Paper II. Given its large volume and fine mass resolution, the MICE-GC simulation also allows an accurate modelling of the lensing observables from upcoming wide and deep galaxy surveys. In the last paper of this series (Paper III), we describe the construction of all-sky lensing maps, following the ‘Onion Universe’ approach, and discuss their properties in the light-cone up to z = 1.4 with sub-arcminute spatial resolution. By comparing the convergence power spectrum in the MICE-GC to lower mass-resolution (i.e. particle mass ∼1011 h −1 M⊙) simulations, we find that resolution effects are at the 5 per cent level for multipoles ℓ ∼ 103 and 20 per cent for ℓ ∼ 104. Resolution effects have a much lower impact on our simulation, as shown by comparing the MICE-GC to recent numerical fits by Takahashi. We use the all-sky lensing maps to model galaxy lensing properties, such as the convergence, shear, and lensed magnitudes and positions, and validate them thoroughly using galaxy shear auto and cross-correlations in harmonic and configuration space. Our results show that the galaxy lensing mocks here presented can be used to accurately model lensing observables down to arcminute scales. Accompanying this series of papers, we make a first public data release of the MICE-GC galaxy mock, the MICECAT v1.0, through a dedicated web-portal for the MICE simulations, http://cosmohub.pic.es, to help developing and exploiting the new generation of astronomical surveys.