By replacing the lens with a thin optical element, lensless imaging enables new applications and solutions beyond those supported by traditional camera design and post-processing, e.g. compact and lightweight form factors and visual privacy. The latter arises from the highly multiplexed measurements of lensless cameras, which require knowledge of the imaging system to recover a recognizable image. In this work, we exploit this unique multiplexing property: casting the optics as an encoder that produces learned embeddings directly at the camera sensor. We do so in the context of image classification, where we jointly optimize the encoder's parameters and those of an image classifier in an end-to-end fashion. Our experiments show that jointly learning the lensless optical encoder and the digital processing allows for lower resolution embeddings at the sensor, and hence better privacy as it is much harder to recover meaningful images from these measurements. Additional experiments show that such an optimization allows for lensless measurements that are more robust to typical real-world image transformations. While this work focuses on classification, the proposed programmable lensless camera and end-to-end optimization can be applied to other computational imaging tasks.