We observed that Lithium Niobate and Lithium Tantalate photonic integrated microresonators exhibit an unexpected Flicker type (i.e. 1/f1.2) scaling in the intrinsic refractive noise spectrum, significantly deviating from the well-established thermorefractive noise theory. We show that this noise is consistent with thermodynamical charge noise, which leads to electrical field fluctuations that are transduced via the strong Pockels effects of electro-optic materials. We demonstrated a Lithium Niobate self-injection locked integrated photonics laser with 56 Hz intrinsic linewidth in a 200 GHz FSR microresonator, achieving the charge-noise limit. Our results establish electrical Johnson-Nyquist noise as the fundamental limitation for Pockels integrated photonics, crucial for determining performance limits for classical and quantum devices. Equally, this observation offers an novel approach to probe mesoscopic electric field fluctuations with exceptional precision.