  While usually cosmological initial conditions are assumed to be Gaussian,
inflationary theories can predict a certain amount of primordial
non-Gaussianity which can have an impact on the statistical properties of the
lensing observables. In order to evaluate this effect, we build a large set of
realistic maps of different lensing quantities starting from light-cones
extracted from large dark-matter only N-body simulations with initial
conditions corresponding to different levels of primordial local
non-Gaussianity strength $f_{\rm NL}$. Considering various statistical
quantities (PDF, power spectrum, shear in aperture, skewness and bispectrum) we
find that the effect produced by the presence of primordial non-Gaussianity is
relatively small, being of the order of few per cent for values of $|f_{\rm
NL}|$ compatible with the present CMB constraints and reaching at most 10-15
per cent for the most extreme cases with $|f_{\rm NL}|=1000$. We also discuss
the degeneracy of this effect with the uncertainties due to the power spectrum
normalization $\sigma_8$ and matter density parameter $\Omega_{\rm m}$, finding
that an error in the determination of $\sigma_8$ ($\Omega_{\rm m}$) of about 3
(10) per cent gives differences comparable with non-Gaussian models having
$f_{\rm NL}=\pm 1000$. These results suggest that the possible presence of an
amount of primordial non-Gaussianity corresponding to $|f_{\rm NL}|=100$ is not
hampering a robust determination of the main cosmological parameters in present
and future weak lensing surveys, while a positive detection of deviations from
the Gaussian hypothesis is possible only breaking the degeneracy with other
cosmological parameters and using data from deep surveys covering a large
fraction of the sky.
