The synthesis and structural characterization of a new type of homologous series of lanthanum cuprates, with the general formula La4+4nCu8+8nO14+8n, is reported. The n=2 and n=3 members, La2Cu2O5 and La8Cu7O19, synthesized in bulk, are stable over very narrow temperature ranges in air and oxygen. Higher members (n > 3) have been observed by electron microscopy. The crystal structure of La2Cu2O5 consists of thin slabs of La2CuO4 sandwiched between CuO planes of complex low-dimensional geometry. The temperature dependent magnetic susceptibilities of La2Cu2O5 and La8Cu7O19 are characteristic of low-dimensional Heisenberg antiferromagnets with a remarkably low exchange coupling energy.