In this study, high-speed mid-infrared Mach-Zehnder electro-optical modulators in x-cut lithium niobate (LN) thin film on sapphire were designed, simulated, and analyzed. The main optical parameters of three types of Mach-Zehnder modulators (MZMs) (residual LN with thickness of 0, 0.5, and 1 mu m) were simulated and calculated, namely, the single-mode conditions, bending loss, separation distance between electrode edge and lithium niobate waveguide edge, optical field distribution, and half-wave voltage-length product. The main radio frequency (RF) parameters of these three types of MZMs, such as characteristic impedance, attenuation constant, RF effective index, and the -3 dB modulation bandwidth were calculated depending on the dimensions of the coplanar waveguide traveling-wave electrodes. The modulations with residual LN thickness of 0, 0.5, and 1 mu m were calculated with bandwidths exceeding 140, 150, and 240 GHz, respectively, and the half-wave voltage-length product achieved was 22.4, 21.6, and 15.1 V cm, respectively. By optimizing RF and optical parameters, guidelines for device design are presented, and the achievable modulation bandwidth is significantly increased.