We investigate an integrated optical circuit on lithium niobate designed to implement the teleportation-based quantum relay scheme for one-way quantum communication at a telecom wavelength. Such an advanced quantum circuit merges for the first time, both optical-optical and electro-optical non-linear functions necessary to implement the desired on-chip single qubit teleportation. On one hand, spontaneous parametric down-conversion is used to produce entangled photon-pairs. On the other hand, we take advantage of two photon routers, consisting of electro-optically controllable couplers, to separate the paired photons and to perform a Bell state measurement, respectively. After having validated all the individual functions in the classical regime, we have performed a Hong-Ou-Mandel (HOM) experiment to mimic a one-way quantum communication link. Such a quantum effect, seen as a prerequisite towards achieving teleportation, has been obtained, at one of the routers, when the chip was coupled to an external single photon source. The two-photon interference pattern shows a net visibility of 80%, which validates the proof of principle of a quantum relay circuit for qubits carried by telecom photons. In case of optimized losses, such a chip could increase the maximal achievable distance of one-way quantum key distribution links by a factor 1.8. Our approach and results emphasize the high potential of integrated optics on lithium niobate as a key technology for future reconfigurable quantum information manipulation.