In self-assembled vertically aligned nanocomposite (VAN) thin films of La2CuO4+δ + LaCuO3, we find from DC magnetic susceptibility measurements, weak signatures of superconductivity at ∼120 K. This compares to a maximum TC of 40 K in bulk La2CuO4+δ. The 120 K signature occurs only when both c-axis and a-axis oriented La2CuO4+δ grains are present in the films. The superconductivity was lost after 3 months of storage but was recovered by annealing in oxygen. From lattice parameter analyses undertaken close to the c/a grain boundaries, it was determined that expansion of the La perovskite block in c-La2CuO4+δ enables the differently oriented grains to join at the interface. This expansion is consistent with the higher TC interfacial region. The work shows a new direction for increasing TC in cuprates - namely careful strain engineering of the crystal structure independently in-plane and out-of-plane.