About a decade ago, in-depth investigations on the behaviour of cold-formed steel (CFS) single-span simply supported lipped channel beams failing in lateral-torsional modes at both room and elevated temperatures were reported at QUT (Queensland Technical University). They revealed a significant underestimation of the lateral-torsional (LT) failure moments by the Direct Strength Method (DSM) global design curve at room temperature, then codified in the Australian/New Zealand and North American specifications. In order to remedy this situation, these authors proposed two novel DSM-based beam strength curve sets, which were found to substantially improve the LT failure moment prediction quality, both at room and elevated temperatures. This work aims at extending the scope of the above investigations, by analysing a visibly larger set of CFS lipped channel beams at elevated temperatures (up to 800 °C), exhibiting (i) various cross-section dimensions and yield stresses, selected to cover wider LT slenderness ranges, (ii) two end support conditions, differing only in the end cross-section wall displacement/rotation and warping restraints (either fully free or fully prevented), and (iii) temperature-dependent steel material properties according with the model prescribed in Part 1-2 of Eurocode 3. The results presented and discussed consist of beam LT post-buckling equilibrium paths and failure moments, obtained through Abaqus shell finite element GMNIA that include critical-mode (LT) initial geometrical imperfections. Lastly, the numerical failure moment data obtained in this work and reported in the literature are used to develop and propose a new unified set of DSM-based strength curves capable of adequately handling beam LT failures at room or elevated temperatures. Since it is shown that the proposed strength curve set provides a quite good LT failure moment prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS beams failing in LT modes at room and elevated temperatures.