Bearing data compression is vital to manage the large volumes of data generated during condition monitoring. In this paper, a novel asymmetrical autoencoder with a lifting wavelet transform (LWT) layer is developed to compress bearing sensor data. The encoder part of the network consists of a convolutional layer followed by a wavelet filterbank layer. Specifically, a dual-channel convolutional block with diverse convolutional kernel sizes and varying processing depths is integrated into the wavelet filterbank layer to enable comprehensive feature extraction from the wavelet domain. Additionally, the adaptive hard-thresholding nonlinearity is applied to remove redundant components while denoising the primary wavelet coefficients. On the decoder side, inverse LWT, along with multiple linear layers and activation functions, is employed to reconstruct the original signals. Furthermore, to enhance compression efficiency, a sparsity constraint is introduced during training to impose sparsity on the latent representations. The experimental results demonstrate that the proposed approach achieves superior data compression performance compared to state-of-the-art methods.