Deep learning has achieved significant success in single hyperspectral image super-resolution (SHSR); however, the high spectral dimensionality leads to a heavy computational burden, thus making it difficult to deploy in real-time scenarios. To address this issue, this paper proposes a novel lightweight SHSR network, i.e., LKCA-Net, that incorporates channel attention to calibrate multi-scale channel features of hyperspectral images. Furthermore, we demonstrate, for the first time, that the low-rank property of the learnable upsampling layer is a key bottleneck in lightweight SHSR methods. To address this, we employ the low-rank approximation strategy to optimize the parameter redundancy of the learnable upsampling layer. Additionally, we introduce a knowledge distillation-based feature alignment technique to ensure the low-rank approximated network retains the same feature representation capacity as the original. We conducted extensive experiments on the Chikusei, Houston 2018, and Pavia Center datasets compared to some SOTAs. The results demonstrate that our method is competitive in performance while achieving speedups of several dozen to even hundreds of times compared to other well-performing SHSR methods.