  Existing nonlinear-optic implementations of pure, unfiltered heralded
single-photon sources do not offer the scalability required for densely
integrated quantum networks. Additionally, lithium niobate has hitherto been
unsuitable for such use due to its material dispersion. We engineer the
dispersion and the quasi-phasematching conditions of a waveguide in the rapidly
emerging thin-film lithium niobate platform to generate spectrally separable
photon pairs in the telecommunications band. Such photon pairs can be used as
spectrally pure heralded single-photon sources in quantum networks. We estimate
a heralded-state spectral purity of ${>}94\%$ based on joint spectral intensity
measurements. Further, a joint spectral phase-sensitive measurement of the
unheralded time-integrated second-order correlation function yields a
heralded-state purity of $(86 \pm 5)\%$.
