© 2017 The Author(s). The presence of neutron stars in at least three ultraluminous X-ray sources is now firmly established and offers an unambiguous view of super-critical accretion. All three systems show long-time-scale periods (60-80 d) in the X-rays and/or optical, two of which are known to be super-orbital in nature. Should the flow be classically super critical, i.e. the Eddington limit is reached locally in the disc (implying surface dipole fields that are sub-magnetar in strength), then the large scale-height flow can precess through the Lense-Thirring effect which could provide an explanation for the observed super-orbital periods. By connecting the details of the Lense-Thirring effect with the observed pulsar spin period, we are able to infer the moment of inertia and therefore equation of state of the neutron star without relying on the inclination of or distance to the system. We apply our technique to the case of NGC 7793 P13 and demonstrate that stronger magnetic fields imply stiffer equations of state.We discuss the caveats and uncertainties, many of which can be addressed through forthcoming radiative magnetohydrodynamic (RMHD) simulations and their connection to observation.