This document is one of a series of white papers from the USQCD Collaboration. Here, we discuss opportunities for Lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent Lattice QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of Lattice QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.