An all-pass racetrack-resonator-Bragg gratings (APRR-BG) on thin-film lithium niobate on insulator (LNOI) based coupling resonant system is proposed to generate tunable electromagnetically induced transparency (EIT)-like transmission. The structure is a normal all-pass racetrack-resonator with two Bragg gratings inscribed within the straight waveguides, which introduces two different optical pathways in essence, inducing EIT-like spectrum as a result. We investigate the linewidth, and tunability of the EIT-like spectrum, and manufacturing tolerance of the resonant system by utilising the transfer matrix method. The simulation results indicate an extremely narrow linewidth of several picometers, and a high voltage sensitivity of 0.338 GHz/V@1550 nm, which indicates potential for optical filter, optical switching, and sensing of the system.