X-ray telescopes based on the lobster-eye principle offer considerable promise for an all-sky monitor mission. The extended cruciform point-spread function of the lobster-eye optic has typically not been a major issue as sources in the classical X-ray band (0.5-3.5keV) at the sensitivities that will be observed are generally point-like and well separated. However, lobster-eye optics may also be used as the basis for an imaging spectrometer for near-earth objects. Such a mission requires that the effect of the lobster-eye point spread function be considered. This paper finds that deconvolution of the point-spread function is feasible at contrast levels as low as 10% for a reasonable orbital configuration and mission duration.