  The high concentrations derived for several strong-lensing clusters present a
major inconsistency between theoretical LambdaCDM expectations and
measurements. Triaxiality and orientation biases might be at the origin of this
disagreement, as clusters elongated along the line-of-sight would have a
relatively higher projected mass density, boosting the resulting lensing
properties. Analyses of statistical samples can probe further these effects and
crucially reduce biases. In this work we perform a fully triaxial
strong-lensing analysis of the 12 MACS clusters at z > 0.5, a complete X-ray
selected sample, and fully account for the impact of the intrinsic 3D shapes on
their strong lensing properties. We first construct strong-lensing mass models
for each cluster based on multiple-images, and fit projected ellipsoidal
Navarro-Frenk-White halos with arbitrary orientations to each mass
distribution. We then invert the measured surface mass densities using Bayesian
statistics. Although the Einstein radii of this sample are significantly larger
than predicted by LambdaCDM, here we find that the mass-concentration relation
is in full agreement with results from N-body simulations. The z > 0.5 MACS
clusters suffer from a moderate form of orientation bias as may be expected for
X-ray selected samples. Being mostly unrelaxed, at a relatively high redshift,
with high X-ray luminosity and noticeable substructures, these clusters may lie
outside the standard concentration-Einstein radius relation. Our results remark
the importance of triaxiality and properly selected samples for understanding
galaxy clusters properties, and suggest that higher-z, unrelaxed
low-concentration clusters form a different class of prominent strong
gravitational lenses. Arc redshift confirmation and weak lensing data in the
outer region are needed to further refine our analysis.
