The increasing demand for image and video data processing, driven by wearable devices, Internet-of-Things, and augmented/virtual reality applications, raises privacy concerns with traditional centralized image classification methods requiring users to upload their data to a cloud server. Recently, lensless imaging devices have emerged as a promising privacy-preserving solution, where image reconstruction requires knowledge of the device's PSF, kept secret from adversaries. However, existing lensless-image-based approaches remain vulnerable to insider threats and new attacks leveraging GAN for PSF estimation. To address these challenges, we propose a novel framework called PPLiC. By transforming raw lensless images into protected sensor measurements, it supports all classification tasks while defending against malicious insiders and GAN-based PSF estimation attacks. PPLiC employs a learning-based approach to identify DCT coefficients with minimal impact on classification accuracy, leveraging the squeeze-and-excitation block, and introduces pseudo-random noises to a small fraction of these coefficients. The index of the selected coefficients and the seed for generating pseudo-random noise collectively serve as the protection key. PPLiC supports classification by utilizing only the selected coefficients, while the reconstruction of the original image requires full knowledge of the protection key. We implemented PPLiC and tested its effectiveness with real-world and simulated lensless images. PPLiC achieves the best satisfying classification performance with an average accuracy of 84.17% and 95.5% on the FlatCam face and simulated DeepFire datasets, respectively. Meanwhile, it offers strong privacy protection since no meaningful image can be reconstructed from the protected sensor measurement using either the original or the GAN-estimated PSF.