Accurate and generalizable ECG classification remains a critical challenge in automated cardiac diagnostics, particularly when dealing with multi-lead signals from heterogeneous sources. In this paper, we propose MuRe-LAT, a Multi-Resolution Lead-Aware Transformer architecture with domain-adaptive normalization designed for robust arrhythmia detection. The model integrates a convolutional stem for local feature extraction, a lead attention module to adaptively weigh channel contributions, dual-scale transformer encoders for capturing both short-term and long-term dependencies, and a domain-specific batch normalization mechanism to mitigate dataset shift. To enhance generalization, MuRe-LAT is pretrained using a masked signal modeling objective. We evaluate the model on two benchmark datasets MIT-BIH Arrhythmia and PTB-XL spanning both ambulatory and clinical ECG recordings. On MIT-BIH, MuRe-LAT achieves an accuracy of 94.0%, a macro-F1 of 88.4, an AUROC of 96.2, and a PR-AUC of 91.6; on PTB-XL, it reaches 88.7% accuracy, 78.1 macro-F1, and 90.5 AUROC. The model also demonstrates strong cross-domain generalization, achieving up to 91.7% accuracy when transferred from PTB-XL to MIT-BIH without retraining. Compared to strong baselines including ResNet-1D, BiLSTM, ECG-BERT, and CardioFormer, MuRe-LAT outperforms or closely matches state-of-the-art results in over 90% of evaluation settings. With only 12.3M parameters and an inference time of 8.4 ms per 10-second ECG window, MuRe-LAT offers a compelling balance between accuracy and efficiency, making it suitable for deployment in real-time clinical and wearable applications.