Abstract: Parton distribution functions (PDFs) and their derived partonic observables, such as generalized parton distributions (GPDs) and distribution amplitudes (DAs), are important physical quantities for studying the internal structure of hadrons and scattering cross-sections in high-energy scattering experiments. Methods such as the large-momentum effective theory (LaMET) provide an effective way to directly calculate the partonic observables on the lattice. In this seminar, I will present a unified factorization matching framework that connects the Euclidean correlations calculated on the lattice with the lightcone correlations that define partonic observables, involving GPDs, PDFs, and DAs. This calculation method can effectively be extended to two-loop level. In addition, I will introduce two new lattice calculation methods for extracting the total gluon helicity contribution to proton spin from lattice QCD.