Lyman-alpha (Lya) surveys are an important tool to constrain the timing and topology of reionization. However, ground-based Lya surveys are not effective at z>8 largely due to the increasing night sky background, and even at z~7 Lya surveys must conduct expensive spectroscopic follow-up of their Lya candidates to eliminate contamination. The Roman Space Telescope's ability to obtain deep near-infrared spectra over a wide field of view offers the opportunity to revolutionize this field. To investigate this further, we have simulated a deep multi-position-angle Roman WFI grism survey and tested our ability to recover z>7 Lya emitters. We show how a novel data cube search technique -- CUBGRISM -- originally developed for GALEX grism data can be applied to Roman grism data to produce a Lya flux-limited sample without the need for a continuum detection. Given our adopted reduction technique, we investigate the impact of altering the number of independent position angles and total exposure time. Our results indicate that a proposed deep Roman grism survey can achieve Lyalpha line depths comparable to the deepest z=7 narrow-band surveys, allowing us to study the evolution of Lya populations and infer the ionization state of the intergalactic medium at cosmic dawn.