Over the last years, sensor-based continuous authentication on mobile devices has achieved great success on personal information protection. These proposed mechanisms, however, require both legal and illegal users' data for authentication model training, which takes time and is impractical. In this paper, we present MAuGANs, a lightweight and practical Memory-Augmented Autoencoder-based continuous Authentication system on smartphones with conditional transformer Generative Adversarial Networks (GANs), where the conditional transformer GANs (CTGANs) are used for data augmentation and the memory-augmented autoencoder (MAu) is utilized to identify users. Specifically, MAuGANs exploits the smartphone built-in accelerometer and gyroscope sensors to implicitly collect users' behavioral patterns. With the normalized legitimate user's sensor data, MAuGANs uses a CTGAN composed of a conditional transformer-based generator and a conditional transformer-based discriminator to create additional training data for the MAu. Then, the MAu is trained on the augmented legitimate user's data. The trained MAu reconstructs the current user data and then calculates the reconstruction error between the reconstructed data and current user data. To carry out user authentication, MAuGANs compares the reconstruction error with a predefined authentication threshold. We evaluate the performance of MAuGANs on our dataset, where our extensive experiments demonstrate that MAuGANs reaches the best authentication performance, when comparing with the representative state-of-the-art methods, by 0.33% EER and 99.65% accuracy on 10 unseen users.