This paper introduces a modified least squares twin support vector machine (LSTSVM) designed to enhance classification accuracy and robustness in the presence of outliers and noisy datasets. Building on the traditional twin SVM (TWSVM) and LSTSVM frameworks, we propose replacing the $L_2$-norm of error variables with the $L_1$-norm to mitigate the influence of extreme values and improve sparsity in the solution. To address the computational challenges of large-scale datasets, we employ the alternating direction method of multipliers (ADMM) to efficiently decompose the optimization problem into smaller subproblems, ensuring scalability and reduced computational costs. Acceleration steps with a guard condition are also integrated to speed up convergence. Experimental evaluations demonstrate the proposed method's superior performance in terms of computational efficiency and classification accuracy compared to TWSVM and traditional LSTSVM, making it a promising solution for real-world applications in classification tasks involving noisy or imbalanced data.