  Lens spaces are a family of manifolds that have been a source of many
interesting phenomena in topology and differential geometry. Their concrete
construction, as quotients of odd-dimensional spheres by a free linear action
of a finite cyclic group, allows a deeper analysis of their structure. In this
paper, we consider the problem of moments for the distance function between
randomly selected pairs of points on homogeneous three-dimensional lens spaces.
We give a derivation of a recursion relation for the moments, a formula for the
$k$th moment, and a formula for the moment generating function, as well as an
explicit formula for the volume of balls of all radii in these lens spaces.
