In this work, we develop a localized model order reduction framework for stationary neutron transport posed on heterogeneous domains. We consider the stationary multi-group neutron transport equation in the combined space-angle phase space and, after discretization in angle and energy, adopt a discontinuous Galerkin (DG) formulation at both the full-order and reduced-order levels. Our target setting is many-query boundary value problems with parametric and random material heterogeneities: the geometry and local cross sections are treated as parameters that may vary independently across modular subdomains. This subdomain-wise independence leads to an effectively high-dimensional parametric space, in which constructing a single global reduced basis that is both small and robust is typically inefficient, motivating a localized reduced basis approach. Inspired by static condensation and generalized multiscale finite element methods, we use a domain decomposition approach in which the global discrete transport operator is assembled from local contributions. On each subdomain, we define outer-to-inner transfer operators that map incoming data prescribed on oversampled external boundaries to traces on internal interfaces, for representative parameter instances. We then exploit the spectral properties of these transfer operators to construct Kolmogorov-optimal reduced spaces for interface unknowns and associated localized basis functions, thereby capturing multiscale spatial structure and local parameter dependence. To obtain parameter-robust local approximation spaces, we employ a spectral greedy strategy over a finite training set of parameter samples. The reduced global transport system is assembled by projecting the full-order DG formulation onto the span of the selected localized bases. The resulting reduced model enables efficient evaluation of neutron transport solutions for many parameter realizations in random heterogeneous media, while providing controlled accuracy for quantities of interest.