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Sources of spectrally engineered photonic states are a key resource in several quantum technologies. Of particular importance are the so-called factorizable biphoton states which possess no spectral entanglement and hence, are ideal for heralded generation of high-purity single photons. An essential prerequisite for generating these states through nonlinear frequency conversion is the control over the group indices of the photonic modes of the source. Here, we show that thin-film lithium niobate on insulator (LNOI) is an excellent platform for this purpose. We design and fabricate periodically poled ridge waveguides in LNOI to demonstrate group index engineering of its guided photonic modes and harness this control to experimentally realize on-chip group index matched type-II sum-frequency generation (SFG) and photon-pair creation through spontaneous parametric down-conversion (SPDC). Also, we numerically study the role of the top cladding layer in tuning the dispersion properties of the ridge waveguide structures and reveal a distinctive difference between the air and silica-clad designs which are currently among the two most common device cladding configurations in LNOI. We expect that these results will be relevant for various classical and quantum applications where dispersion control is crucial in tailoring the nonlinear response of the LNOI-based devices.