Good quality bulk size single crystals of inverse soluble lithium sulphate monohydrate (LSMH) have been grown by the modified Sankaranarayanan–Ramasamy (SR) method. A growth rate as high as 3 mm per day has been obtained for LSMH growth without substantially degrading the optical quality. The rocking curve recorded using the high resolution X-ray diffraction (HRXRD) technique reveals that the crystals grown by this method have a high degree of crystalline perfection. The optical quality of the crystals was studied using an UV-vis-NIR spectrum and the optical constants of the LSMH crystals were calculated. The laser damage threshold value of the grown crystals has been determined using a nanosecond Nd:YAG laser operating at 532 nm. Photoconductivity studies of the grown LSMH crystals reveal a positive photoconductivity behaviour of the grown crystals. The photoluminescence spectrum of the LSMH crystals shows a prominent emission peak at 373 nm. The third order non-linear optical properties of the LSMH crystals were investigated in detail by the Z-scan technique using a He–Ne laser operating at 632.8 nm. The non-linear refractive index (n2), non-linear absorption coefficient (β) and third order non-linear susceptibility (χ(3)) of the LSMH crystals were calculated.