The rise of Extended Reality (XR) requires efficient streaming of 3D online worlds, challenging current 3DGS representations to adapt to bandwidth-constrained environments. This paper proposes LapisGS, a layered 3DGS that supports adaptive streaming and progressive rendering. Our method constructs a layered structure for cumulative representation, incorporates dynamic opacity optimization to maintain visual fidelity, and utilizes occupancy maps to efficiently manage Gaussian splats. This proposed model offers a progressive representation supporting a continuous rendering quality adapted for bandwidth-aware streaming. Extensive experiments validate the effectiveness of our approach in balancing visual fidelity with the compactness of the model, with up to 50.71% improvement in SSIM, 286.53% improvement in LPIPS, and 318.41% reduction in model size, and shows its potential for bandwidth-adapted 3D streaming and rendering applications.