Lower-limb exoskeleton robots play an important role in rehabilitation training and walking assistance, where accurate lower-limb joint angle prediction is a key technology for achieving natural and coordinated gait. However, since surface electromyography (sEMG) signals are susceptible to individual differences and variations in movement patterns, achieving cross-task generalization for joint angle prediction remains a major challenge. To address the above issues, this paper proposes a cross-task generalization-oriented multi-joint angle prediction framework for the lower limb, which includes a non-redundant muscle synergy feature extraction algorithm and a joint angle prediction network with cross-speed and cross-subject generalization capabilities. First, the feature extraction algorithm employs non-negative matrix factorization to extract activation coefficient matrices from sEMG signals, and further uses the Uniform Manifold Approximation and Projection algorithm for nonlinear dimensionality reduction to obtain low-dimensional features with higher discriminative power as model inputs. Second, the joint angle prediction network extracts cross-task shared features through pre-training and leverages a small number of samples from new tasks for fine-tuning, enabling rapid adaptation to new tasks. Based on a self-constructed dataset and a public dataset, this paper conducts feature extraction method comparison experiments, model ablation experiments, and cross-speed and cross-subject generalization experiments. Experimental results show that in cross-speed experiments on the self-constructed dataset, the prediction errors of hip and knee joint angles range from 1.703 1° to 2.790 4°, with correlation coefficients all exceeding 0.98. Compared with baseline methods, the proposed method achieves significant improvements in both prediction accuracy and stability, demonstrating its effectiveness and generalizability. Finally, physical experiments on exoskeleton-assisted walking are conducted, further validating the feasibility and application potential of the proposed method in practical lower-limb exoskeleton applications.