<p>The Lyra geometry provides an interesting approach to develop purely geometrical scalar-tensor theories. Here we present a theory on Lyra manifolds which contains generalizations of both Brans-Dicke gravity and Einstein-Gauss-Bonnet scalar-tensor theory. We show that the symmetry group of gravitational theories on the Lyra geometry comprises not only coordinate transformations but also local transformations of length units, so that the Lyra function is a conformal factor which locally fixes the unit of length. The Lyra geometry is thus the generalization of Riemannian geometry which properly includes spacetime-dependent length units. By performing a Lyra transformation to a frame in which the length unit is globally fixed, we show that General Relativity (GR) is obtained from the Lyra Scalar-Tensor Theory (LyST). Through the same procedure, it is found that Brans-Dicke gravity and the Einstein-Gauss-Bonnet scalar-tensor theory are obtained from their Lyra counterparts. It might be possible that any known scalar-tensor theory can be naturally geometrized by considering a particular Lyra frame, for which the scalar field is the function which locally controls the unit of length. The Jordan-Einstein frame conundrum is also assessed from the perspective of Lyra transformations: we show that the Lyra geometry makes explicit that the two frames are only different representations of the same theory, so that in the Einstein frame the unit of length varies locally. The Lyra formalism is then better suited for exploring scalar-tensor gravity, since in its well-defined structure the conservation of the energy-momentum tensor and geodesic motion are assured in the Einstein frame.</p>