Guided Mode Resonant Filters (GMRFs) have long been studied as a support surface for nonlinear optical interactions due to their intrinsically high Q-factor. However, their operation relies on a non-localized and large-area guided mode that limits the achievable power density and requires complex phase-matching approaches. Conversely, photonic crystal nano-cavities have shown promising results due to both their high-Q factors to enhance the pump field and their localized nature that allows phase-matching-free implementation and high power density excitation. However, their intrinsic small size restricts the supported input power and hinders the coupling efficiency of the pump into the mode. In this paper, we report the first experimental demonstration of continuous-wave second harmonic generation in a Cavity-Resonator Integrated Grating Filter (CRIGF). This intermediary device, which can be described as a cavity-enhanced finite-size GMRF or, equivalently, as a low-index-contrast photonic crystal micro-cavity, will be shown to offer a practical route to nonlinear interactions with viable power (<20 mW) and excitation conditions (surface excitation with a ~10-μm-waist spot size). In practice, the devices under study make use of a lithium-niobate on insulator (LNOI) waveguide with a nanostructured silicon nitride upper cladding as a pragmatic way to implement a high second-order nonlinearity platform with established processing technology. The already-demonstrated versatility of the CRIGF design (demonstrated at wavelengths of 850 nm using S3iN4/SiO2 platform, 4.5 μm with the GaAs/AlGaAs technology and, here, at 1.55 μm with the LiNbO3 platform) coupled to the electro-optical tuning afforded by lithium niobate system makes this approach extremely promising for pixelated non-linear systems.