Two-dimensional (2D) lateral heterojunctions between different transition metal dichalcogenides (TMDCs) have been realized in recent years. Homogeneous semiconducting TMDC layers are characterized by a topological invariant, their in-plane electric polarization. It suggests the possibility of one-dimensional (1D) metallic states at heterojunctions where the value of the invariant changes. We study such lateral 2D TMDC junctions by means of first-principles calculations and show that 1D metallic states emerge even in cases where the different materials are joined epitaxially. We find that the metallicity does not depend on structural details, but, as the invariant is protected by spatial symmetry only, it can be upset by breaking the symmetry. Indeed, 1D charge- and spin-density wave instabilities appear spontaneously, making 2D TMDC heterojunctions ideal systems for studying 1D systems.