Permittivity modulation in nonlocal metasurfaces provides an effective route for unlocking radiative coupling of symmetry-protected bound states in the continuum (BICs), enabling unprecedented dynamic control over resonant light-matter interactions. Here, we present a periodically poled lithium niobate metasurface platform that leverages spatially antisymmetric electro-optic responses induced by the Pockels effect to achieve continuous control of radiative coupling. Distinctively, the electro-optic asymmetry introduces an independent and continuously tunable perturbation channel, enabling post-fabrication control of the radiative coupling. By interfering with the radiation amplitude induced by unintended structural asymmetry, it enables compensation of geometry-induced radiation leakage to a large extent and thereby restores high-Q resonances. Concurrently, the domain-engineered architecture intrinsically embeds nonlinear optical functionality, operating as a tunable χ⁽²⁾ grating that enables large-angle (71.4°) second-harmonic generation with electrically controlled emission. We demonstrate high nonlinear switching contrast exceeding 22 dB under moderate electric fields (≤20 V/μm), bridging high-Q resonance engineering with nonlinear photonics to provide a unified platform for next-generation on-chip optical switches, dynamic filters, and frequency converters.