Optical, dielectric, and thermal properties of lithium sulphate monohydrate crystals grown by slow evaporation method have been studied. The crystal structure was resolved by direct methods using single crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0174. Plasma energy, Penn gap, Fermi energy and electronic polarizability of the grown crystal were calculated from single crystal XRD data. The electronic polarizability of lithium sulfate monohydrate was also calculated and compared with the theoretical data using Clausius-Mossotti equation. Optical band gap calculated from optical data for the grown crystal is 4.49 eV. Fourier Transform Infrared Spectroscopy study confirmed the presence of water in the crystal structure. The AC conductivity, dielectric constant and dielectric loss of the grown crystal were systemically investigated, showing a peak at about 130 °C which could be attributed to the water molecules in the crystal structure. The anomalous dielectric properties shown by the crystal have been correlated with its thermal behavior. The title crystal obeys Jonscher’s power law relation; σ(ω) = σo+ Aωs, with temperature dependent exponent s < 1. The activation energy calculated for the material is 0.24 eV and suggests protonic conduction by hopping mechanism in addition to cationic conduction by lithium ions. The micro-indentation study was also carried out which revealed that the crystal belongs to a category of soft materials.