Recently, as deep learning technologies have received much attention for their great potential in extracting the principal components of data, there have been many efforts to apply them to the Channel State Information (CSI) feedback overhead problem, which can significantly limit Multi-Input Multi-Output (MIMO) beamforming gains. Unfortunately, since most compression models can quickly become outdated due to channel variation, timely model updates are essential for reflecting the current channel conditions, resulting in frequent additional transmissions for model sharing between transceivers. In particular, the heavy network models employed by most previous studies to achieve high compression gains exacerbate the impact of the overhead, eventually cancelling out the benefits of deep learning-based CSI compression. To address these issues, in this paper, we propose Lightweight CSI Feedback (LCF), a new lightweight CSI feedback scheme. LCF fully utilizes autoregressive Long Short-Term Memory (LSTM) to generate CSI predictions and uses them to train the autoencoder, so that the compression model could work effectively even in highly dynamic wireless channels. In addition, 3D convolutional layers are directly adopted in the autoencoder to capture diverse types of channel correlations in three dimensions. Extensive experiments show that LCF achieves a lower CSI compression error in terms of the Mean Squared Error (MSE), using only about 10% of the overhead of existing approaches.