We expand upon the efforts of Joyce et al. (2013), who computed the modulation potential at the Moon using measurements from the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument on the Lunar Reconnaissance Orbiter (LRO) spacecraft along with data products from the Earth-Moon-Mars Radiation Environment Module (EMMREM). Using the computed modulation potential, we calculate galactic cosmic ray (GCR) dose and dose equivalent rates in the Earth and Mars atmospheres for various altitudes over the course of the LRO mission. While we cannot validate these predictions by directly comparable measurement, we find that our results conform to expectations and are in good agreement with the nearest available measurements and therefore may be used as reasonable estimates for use in efforts in risk assessment in the planning of future space missions as well as in the study of GCRs. PREDICCS (Predictions of radiation from REleASE, EMMREM, and Data Incorporating the CRaTER, COSTEP, and other solar energetic particles measurements) is an online system designed to provide the scientific community with a comprehensive resource on the radiation environments of the inner heliosphere. The data products shown here will be incorporated into PREDICCS in order to further this effort and daily updates will be made available on the PREDICCS website (http://prediccs.sr.unh.edu).