Next generation high-precision neutrino scattering experiments have the goal of measuring the as-of-yet unknown parameters governing neutrino oscillation. This effort is hampered by the use of large nuclear targets: secondary interactions within a nucleus can confuse the interpretation of experimental data, leading to ambiguities about the initial neutrino interaction in scattering events. The distribution of energies for neutrino events must instead be inferred from the responses of a sum of dissimilar event topologies. For this reason, precise neutrino cross sections on nucleon targets are of vital importance to the neutrino oscillation experimental program. On the other hand, the necessary experimental data for neutrino scattering with elementary targets are scarce because of the weak interaction cross section, which leads to poorly-constrained nucleon and nuclear cross sections. Lattice QCD is uniquely positioned to provide the requisite nucleon amplitudes needed to enable high-precision oscillation experiments. In particular, LQCD has the ability to probe axial matrix elements that are challenging to isolate or completely inaccessible to experiments. In these proceedings, I will discuss some of my work to quantify neutrino cross sections with realistic uncertainty estimates, primarily focusing on neutrino quasielastic scattering and the nucleon axial form factor. I will also outline how the needs of next-generation neutrino oscillation experimental programs can be met with modern dedicated LQCD computations.