As an important tool for exploring the “terahertz gap” in the electromagnetic spectrum, terahertz time-domain spectroscopy has shown broad application prospects in materials science, biomedicine, nondestructive testing, and related fields. It has also been increasingly introduced into physics laboratory teaching as a frontier scientific topic. However, teaching platforms based on commercial terahertz time-domain spectrometers usually provide students with limited operational freedom. Their experimental procedures tend to be fixed, and students often follow prescribed steps mechanically, resulting in insufficient understanding of key principles. In this paper, an open teaching platform is developed based on a self-built terahertz time-domain spectroscopy system. The platform integrates terahertz generation using photoconductive antennas and electro-optic detection, with particular emphasis on the basic principles and technical implementation of lock-in amplification for weak-signal measurement. It guides students to understand signal extraction and noise suppression in practical experimental scenarios. Students can independently set sampling parameters, write code to perform Fourier-transform analysis of raw data, and complete the full analysis from time-domain waveforms to absorption spectra, thereby deepening their understanding of the basic principles of terahertz time-domain spectroscopy and the lock-in amplification process. Using lactose monohydrate as a sample, the platform successfully detects its characteristic absorption peaks, verifying the feasibility of terahertz time-domain spectroscopic analysis and application. The construction model and teaching practice of this platform provide a useful reference for the development and application of similar terahertz experimental teaching platforms.