It is often taken for granted that Generalized Parton Distributions (GPDs) are defined in the "symmetric" frame, where the transferred momentum is symmetrically distributed between the incoming/outgoing hadrons. However, such frames pose more computational challenges for the lattice QCD practitioners. In this talk, we lay the foundation for lattice QCD calculations of GPDs in non-symmetric frames, where the transferred momentum is not symmetrically distributed between the incoming/outgoing hadrons. The novelty of our approach relies on the parameterization of the matrix elements in terms of the so-called Generalized Ioffe-time Distributions (ITD), which helps in not only isolating but also reducing part of the higher-twist contaminations as a byproduct. This work opens possibilities for faster and more effective computations of GPDs.