Due to the constraints of reduced radiation doses, low-dose computed tomography (LDCT) images frequently suffer from increased noise levels. To address this challenge, we developed the LCTU-Net, a network that incorporates a Lipschitz continuous transformer to enhance the capability of feature extraction. This new approach replaces traditional Transformer components, improving the efficiency of loss reduction and achieving lower loss levels. The U-Net architecture integrated within LCTU-Net plays a crucial role in effectively reducing noise interference in the images. Experimental results have demonstrated that LCTU-Net significantly outperforms existing denoising technologies, particularly in its ability to preserve intricate image details while effectively reducing noise.