Lateral walking gait phase recognition and prediction are the premise of hip exoskeleton application in lateral resistance walk exercise. We presented a fusion network with stacked denoise autoencoder and meta learning (SDA-NN-ML) to recognize gait phase and predict gait percentage from IMU signals. Experiments were conducted to detect the four lateral walking gait phases and predict their percentage across different speeds. The performance of SDA-NN-ML and Support Vector Machine (SVM), Adaptive Boosting (AdaBoost) and Long Short Term Memory (LSTM) were evaluated. The cross-subject recognition accuracy of SDA-NN-ML (89.94%) decreased by 4.62% compared to the training accuracy, which outperformed SVM (8.60%), AdaBoost (5.61%), and LSTM (7.12%). For real-time and cross-subject prediction of gait phase percentage, the RMSE of SDA-NN-ML (0.2043) outperformed that of a single regression network (0.2426). With a signal noise ratio of 100:30, the cross-subject recognition accuracy decreased by a mere 5.70%, while the prediction result (RMSE) of SDA-NN-ML increased by 0.0167 when compared to the noise-free results. SDA-NN-ML demonstrates a stable multi-step-ahead prediction ability with an accuracy higher than 82.50% and an RMSE of less than 0.23 when the ahead time is less than 200 ms. The results demonstrated that the proposed method has high accuracy and robust performance in lateral walking gait recognition and prediction.