In Cloud 3D, such as Cloud Gaming and Cloud Virtual Reality (VR), image frames are rendered and compressed (encoded) in the cloud, and sent to the clients for users to view. For low latency and high image quality, fast, high compression rate, and high-quality image compression techniques are preferable. This paper explores computation time reduction techniques for learned image compression to make it more suitable for cloud 3D. More specifically, we employed slim (low-complexity) and application-specific AI models to reduce the computation time without degrading image quality. Our approach is based on two key insights: (1) as the frames generated by a 3D application are highly homogeneous, application-specific compression models can improve the rate-distortion performance over a general model; (2) many computer-generated frames from 3D applications are less complex than natural photos, which makes it feasible to reduce the model complexity to accelerate compression computation. We evaluated our models on six gaming image datasets. The results show that our approach has similar rate-distortion performance as a state-of-the-art learned image compression algorithm, while obtaining about 5x to 9x speedup and reducing the compression time to be less than 1 s (0.74s), bringing learned image compression closer to being viable for cloud 3D. Code is available at https://github.com/cloud-graphics-rendering/AppSpecificLIC.