Wavelength transduction of single-photon signals is indispensable to networked quantum applications, particularly those incorporating quantum memories. Lithium niobate nanophotonic devices have demonstrated favorable linear, nonlinear, and electro-optical properties to deliver this crucial function while offering superiror efficiency, integrability, and scalability. Yet, their quantum noise level--an crucial metric for any single-photon based application--has yet to be understood. In this work, we report the first study with the focus on telecom to near-visible conversion driven by a telecom pump of small detuning, for practical considerations in distributed quantum processing over fiber networks. Our results find the noise level to be on the order of $10^{-4}$ photons per time-frequency mode for high conversion, allowing faithful pulsed operations. Through carefully analyzing the origins of such noise and eachs dependence on the pump power and wavelength detuning, we have also identified a formula for noise suppression to $10^{-5}$ photons per mode. Our results assert a viable, low-cost, and modular approach to networked quantum processing and beyond using lithium niobate nanophotonics.