To increase the redshift range and look-back time over which the radio luminosity function can be measured directly, we identified 1157 galaxies in the Las Campanas Redshift Survey (LCRS, Cat. <VII/203>) having isophotal (red) magnitudes m_ISO_<=18.0 with radio sources brighter than 2.5mJy/beam in the 1.4GHz NRAO VLA Sky Survey (NVSS, 1998AJ....115.1693C). Since the NVSS has 45" FWHM angular resolution, these radio and optical limits include nearly all LCRS galaxies with 1.4GHz luminosities L>=10^22.4^W/Hz at z~0.05 to L>=10^23.6^W/Hz at z~0.2. The mean redshift <z>~0.14 of the radio-detected galaxies is higher than the mean redshift <z>~0.10 of the optical sample. This indicates that, statistically, the radio emission was detected from galaxies with the highest optical luminosities. Of the 1157 galaxies, 261 were also identified with far-infrared (FIR) sources in the IRAS Point Source Catalog and Faint Source Catalog. The principal radio energy sources in all identified galaxies were classified as either "starburst" or "AGN" on the basis of their FIR-radio flux ratios, FIR spectral indices, and radio-optical flux ratios. We show that the radio-optical flux ratio can be effectively used to classify the dominant energy source for the radio emission even if FIR fluxes and radio morphological data are not available.