The 2ν３ band R3 branch (6 046.95 cm-1) is the most commonly used band in near-infrared methane detection. The three spectral lines of the R3 branch are very close to each other, and the Lorentzian profile of a spectral line is usually used to describe its spectral shape to correct the second harmonic peak error caused by temperature and pressure. However, the error caused by the Lorentzian profile itself has not received enough attention. In this paper, the TDLAS system is simulated and analyzed as follows. The low-frequency sawtooth wave and the high-frequency sine wave are superimposed to modulate the laser. After the detection gas is absorbed, it is then demodulated by digital lock-in amplification and low-pass filtering, and finally, the second harmonic signal normalized by the first harmonic is obtained by the rotating coordinate system method. By comparing the influence of the Lorentzian profile approximation of a single spectral line and the Voigt profile of three spectral lines on the second harmonic, the second harmonic error caused by the Lorentzian profile approximation under the conditions of temperature and pressure changes is analyzed. The result indicates that: (1) When the pressure and temperature change, the peak error of the second harmonic of the Lorentzian profile is smaller than the average minimum value error; (2) The peak value error of the second harmonic caused by the Lorentzian profile approximation increases significantly with the decrease of pressure. When the temperature is 298 K, and the pressure is reduced to 0.2 atm, the peak value error of the second harmonic of methane gas brought by the Lorentzian profile approximation reaches 65.5%; (3) The second harmonic spectral shape is measured by parameters such as peak-to-valley ratio and harmonic width. When the temperature is 298 K, and the pressure is less than 0.8 atm, the peak-valley ratio error is more than 4.5%, and when the pressure is 1 atm, and the temperature is more than 380 K, the peak-to-valley rate error is more than 4.8%. Since the second harmonic spectral shape error is more sensitive to the peak-to-valley rate parameter, for methane gas at 6 046.95 cm-1, the Lorentzian profile is difficult to apply to the calibration-free algorithm; (4) The Lorentzian profile approximation error decreases as the modulation coefficient increases. When the temperature is 298 K and the pressure is 1 atm, the modulation current is greater than 2.2 mA (corresponding to the modulation factor of 1.33), the second harmonic peak error, peak-to-valley rate error and width error are all less than 3.5%. The proposed Lorentzian profile error analysis method has a certain reference significance for studying the methane detection error of TDLAS caused by profile approximation in the environment of temperature and pressure changes. It can also be extended to TDLAS detection of other gas multi-line bands.