  In this work, we study the existence of gradient (proper) CKVs in locally
rotationally symmetric spacetimes (LRS), those CKVs in the space spanned by the
tangent to observers' congruence and the preferred spatial direction, allowing
us to provide a (partial) characterization of gradient conformally static
(GCSt) LRS solutions. Irrrotational solutions with non-zero spatial twist admit
an irrotational timelike gradient conformal Killing vector field and hence are
GCSt. In the case that both the vorticity and twist vanish, that is,
restricting to the LRS II subclass, we obtain the necessary and sufficient
condition for the spacetime to admit a gradient CKV. This is given by a single
wave-like PDE, whose solutions are in bijection to the gradient CKVs on the
spacetime. We then introduce a characterization of these spacetimes as GCSt
using the character of the divergence of the CKV, provided that the metric
functions of the spacetimes obey certain inequalities.
