A method to solve minimum-lap-time problems using quasi-steady-state models and free (i.e. not predetermined) trajectory on two-dimensional tracks has been recently proposed. This work describes the extension of the method to three-dimensional tracks and builds upon g-g-g diagrams (instead of the standard g-g), to account for the effects of three-dimensionality. The main features of car and motorcycle g-g-g diagrams are discussed, to get insight into the main effects of three-dimensionality and to suggest a convenient parametrisation for the subsequent optimal control problem (OCP), whose size is not affected by the complexity of the vehicle model employed to generate the g-g-g diagrams. The application of the method to the Mugello and Barcelona-Catalunya circuits is given, with vehicle datasets resembling those of a race motorcycle (MotoGP) and a race car (Formula One). The results obtained are in line with those reported in the literature using full-dynamic models, yet such dynamic models are generally associated with the solution of much larger OCP.