  Over the last decade there were significant advances in the understanding of
quantum gravity coupled to point particles in 3D (2+1-dimensional) spacetime.
Most notably it is emerging that the theory can be effectively described as a
theory of free particles on a momentum space with anti-deSitter geometry and
with noncommutative spacetime coordinates of the type $[x^{\mu},x^{\nu}]=i
\hbar \ell \varepsilon^{\mu\nu}_{\phantom{\mu\nu}\rho} x^{\rho}$. We here show
that the recently proposed relative-locality curved-momentum-space framework is
ideally suited for accommodating these structures characteristic of 3D quantum
gravity. Through this we obtain an intuitive characterization of the
DSR-deformed Poincar\'e symmetries of 3D quantum gravity, and find that the
associated relative spacetime locality is of the type producing dual-gravity
lensing.
