LaTiOx compounds are structurally related to perovskites and there are two known phases. The first, x=3.50, is a 2D layered-type ferroelectric. The second, x=3.00, is a weak ferromagnet with a 3D orthorhombic distorted perovskite structure. 20 samples with varying oxygen stoichiometry between these end members were prepared by floating zone melting, and then characterized by means of X-ray powder diffraction, electron microscopy, thermogravimetric analysis, resistivity and magnetic measurement. A phase diagram is established which displays the following physical and structural properties. A structural phase boundary at x=3.20 separates a new series of 2D layered structures from the 3D orthorhombic one. The former series represents the first conducting titanium oxides with a 2D layered structure to be reported. At x=3.10 a phase boundary exists between a metallic and a weak ferromagnetic state where the magnetic transition temperature Tc can be sensitively tuned by the oxygen stoichiometry x. Samples with Tc between 100 K and 130 K exhibit a metal-semiconductor transition whereas samples with higher Tc, up to 149 K, are semiconductors between room temperature and 4.2 K.