Drawing on theoretical insights, we advocate an error-based thresholding (EBT) mechanism for learned ISTA (LISTA), which utilizes a function of the layer-wise reconstruction error to suggest a specific threshold for each observation in the shrinkage function of each layer. We show that the proposed EBT mechanism well disentangles the learnable parameters in the shrinkage functions from the reconstruction errors, endowing the obtained models with improved adaptivity to possible data variations. With rigorous analyses, we further show that the proposed EBT also leads to a faster convergence on the basis of LISTA or its variants, in addition to its higher adaptivity. Extensive experimental results confirm our theoretical analyses and verify the effectiveness of our methods.