A new, to the best of our knowledge, method of generating interference patterns based on a non-orthogonal Lloyd's mirror interferometer with a spatial phase modulation is proposed. In the proposed method, a spatial light modulator (SLM) is introduced to a conventional non-orthogonal Lloyd's mirror interferometer so that arbitrary interference patterns, such as line interference patterns with varied line-spacing or two-dimensional patterns, can be generated by controlling the wavefronts of the laser beams at each position on the substrate. In this paper, as the first step of the research, the feasibility of the proposed method is theoretically confirmed by calculating interference patterns to be obtained when a spatial modulation of the phase delay is applied to the laser beams. A prototype of a non-orthogonal one-axis Lloyd's mirror interferometer with an SLM in its optical path is also designed and constructed. Some basic experiments are carried out to demonstrate the feasibility of the generation of interference patterns having varied line-spacing and two-dimensional patterns by the proposed method.