Two new lanthanum copper phosphides, LaCu1+xP2 and LaCu4P3, were synthesized from elements. Their crystal structures were determined by means of single-crystal X-ray diffraction. LaCu1+xP2 crystallizes in a complex crystal structure, a derivative of the HfCuSi2 structure type, in the space group Cmmm (No. 65) with unit cell parameters of a = 5.564(3) angstrom, b = 19.96(1) angstrom, c = 5.563(3) angstrom, and Z = 8. Its crystal structure features disordered Cu2xP2 layers alternated with fully ordered PbO-like Cu2P2 layers. The Cu-P layers are separated by La counter-cations. The Cu2xP2 layers are composed of rectangular P-4 polyphosphide rings connected by partially occupied Cu atoms. Investigations of the electrical resistivity and Seebeck thermopower for LaCu1+xP2 reveal metallic-type behavior with holes as the main charge carriers. LaCu1+xP2 exhibits unexpectedly low thermal conductivity presumably because of disorder in the Cu2xP2 layers. LaCu4P3 crystallizes in a new structure type, in the tetragonal space group P-4/nmm (No. 129) with unit cell parameters of a = 5.788(2) angstrom, c = 7.353(2) angstrom, and Z = 2. Its crystal structure features distorted square nets of Cu atoms within the Cu4P3 slabs. Electron localization function analysis indicates that both P atoms in LaCu4P3 have 1 + 4 coordination involving multicenter Cu-P bonding. According to the density of states and band structure, LaCu4P3 is predicted to be a metallic conductor.