Lutetium-177 has been extensively used in cancer treatment by irradiating the enriched ¹⁷⁶Lu target. Laser Isotope Separation (LIS) of ¹⁷⁶Lu with a three-step selective photoionisation scheme is reported on a laboratory scale, which depends on the availability of directional neutral atomic beams of lutetium vapour. This study focuses on the suitability of an e-beam evaporator for the generation of lutetium metal vapour for the LIS process. Electron beam evaporation trials were carried out for lutetium to measure the metal vapour flux and spatial vapour distribution with e-beam power in the range of 400 W to 600 W. At the height of 195 mm from the source, the vapour flux was ~0.6 mg/cm^2·min at e-beam power of 400 W and ~2.5 mg/cm^2·min at 600 W. Electron beam evaporation of the lutetium block resulted in a keyhole of ~15 mm depth. Complete ingot melting was not observed, restricting the useable fraction for vapour generation. A computational model was prepared to predict the maximum molten charge fraction and validated with the experimental data. Improvisations such as hybrid source, bulk evaporation and usage of an alloy are suggested for the development of an atomic vapour source of lutetium.