Lightning is the primary natural cause of wildfires in mid- to high-latitude forests, and it is increasing in frequency under climate change. Traditional fire danger forecasts, reliant on standard meteorological data, often fail to capture extreme events and future risk. To address this issue, we integrate extreme climate indices with meteorological, vegetation, soil, and topographic data, and apply four machine learning methods to build probabilistic models for lightning fire occurrence. The results show that incorporating extreme climate indices significantly improves model performance. Among the models, XGBoost achieved the highest accuracy (87.4%) and AUC (0.903), clearly outperforming traditional fire weather indices (accuracy 60%–71%). Model interpretation with SHapley Additive exPlanations (SHAP) further revealed the driving mechanisms and interaction effects of extreme factors. Extreme temperature and precipitation indices contributed nearly 60% to fire occurrence, with growing season length (GSL), minimum of daily maximum temperature (TXn), diurnal temperature range (DTR), and warm spell duration index (WSDI) identified as key drivers. In contrast, heavy precipitation indices exerted a suppressing effect. Compound hot and dry conditions amplified fuel aridity and markedly increased ignition probability. This interpretable framework improves short-term lightning fire prediction and offers quantitative support for risk warning and resource allocation in a warming climate.