  In this article, we construct novel explicit solutions for nonlinear
Schr\"odinger systems with spatially inhomogeneous nonlinearity by means of the
Lie symmetry method. We focus the attention to solutions with non-trivial
phase, which have been scarcely considered in the related literature. To get
started, the theoretical method based on Lie symmetries is exposed, thus
reducing the problem to the integrability of an ODE. The non-trivial phase
introduces a singular term into the ODE. Then, the method is used to construct
new families of analytical solutions. Some illustrative examples are provided.
