  It was recently realized that Planck-scale momentum-space curvature, which is
expected in some approaches to the quantum-gravity problem, can produce
dual-curvature lensing, a feature which mainly affects the direction of
observation of particles emitted by very distant sources. Several gray areas
remain in our understanding of dual-curvature lensing, including the
possibility that it might be just a coordinate artifact and the possibility
that it might be in some sense a by product of the better studied
dual-curvature redshift. We stress that data reported by the IceCube neutrino
telescope should motivate a more vigorous effort of investigation of
dual-curvature lensing, and we observe that studies of the recently proposed
"$\rho$-Minkowski noncommutative spacetime" could be valuable from this
perspective. Through a dedicated $\rho$-Minkowski analysis, we show that
dual-curvature lensing is not merely a coordinate artifact and that it can be
present even in theories without dual-curvature redshift.
