Learned image compression (LIC) methods often employ symmetrical encoder and decoder architectures, evitably increasing decoding time. However, practical scenarios demand an asymmetric design, where the decoder requires low complexity to cater to diverse low-end devices, while the encoder can accommodate higher complexity to improve coding performance. In this paper, we propose an asymmetric lightweight learned image compression (AsymLLIC) architecture with a novel training scheme, enabling the gradual substitution of complex decoding modules with simpler ones. Building upon this approach, we conduct a comprehensive comparison of different decoder network structures to strike a better trade-off between complexity and compression performance. Experiment results validate the efficiency of our proposed method, which not only achieves comparable performance to VVC but also offers a lightweight decoder with only 51.47 GMACs computation and 19.65M parameters. Furthermore, this design methodology can be easily applied to any LIC models, enabling the practical deployment of LIC techniques.