While point cloud-based applications are gaining traction due to their ability to provide rich and immersive experiences, they critically need efficient coding solutions due to the large volume of data involved, often many millions of points per object. The JPEG Pleno Learning-based Point Cloud Coding standard, as the first learning-based coding standard for static point clouds, has set a foundational framework with very competitive compression performance regarding the relevant conventional and learning-based alternative point cloud coding solutions. This paper proposes a novel lightweight point cloud geometry coding model that significantly reduces the complexity of the standard, which is essential for the broad adoption of this coding standard, particularly in resource-constrained environments, while simultaneously achieving small average compression efficiency benefits. The novel coding model is based on the pioneering adoption of a compressed domain approach for the super-resolution model, in addition to a major reduction of the number of latent channels. A reduction of approximately 70% in the total number of model parameters is achieved while simultaneously offering slight average compression performance gains for the JPEG Pleno Point Cloud coding dataset.