Large area fiber array telescopes are a relatively modern development in the long history of telescope design and effectively create a single large equivalent aperture by combining many smaller unit telescopes at a fraction of the cost. In this study a spectrograph optical design is demonstrated that utilizes photonic lanterns in the input fiber feed for the Large Fiber Array Spectroscopic Telescope (LFAST) design concept, where photonic lanterns provide a simplified approach to the fiber feed originally proposed for LFAST. Conservation of etendue is applied to derive the relationship between slit size and photonic lantern ratio, and classical echelle spectrograph designs are explored. A high-resolution spectrograph for LFAST is shown to not be feasible due to the large number of input fibers that result in a large required cross-dispersion within the constraint of practical and cost-effective optical component sizes. An alternative approach of splitting the slit length and replicating spectrographs is explored, and an optimal choice of four spectrographs with a photonic lantern ration of four is determined. Even with this approach, detailed spectrograph component designs show that the spectrograph does not meet the resolution requirements and is fundamentally limited by design constraints imposed by component sizes. Alternative layouts and design decisions to improve optical performance are surveyed for future design research, and include white pupil optics, echelle grating design considerations, spectral arm splitting, and use of reflective and catadioptric systems with aspheric surfaces. While these show promise for improving the spectrograph performance, the design is demonstrated to still be challenging and will likely require innovative approaches to meet the high-resolution design goals.