Autoregressive (AR) models, the theoretical performance benchmark for learned lossless image compression, are often dismissed as impractical due to prohibitive computational cost. This work re-thinks this paradigm, introducing a framework built on hierarchical parallelism and progressive adaptation that re-establishes pure autoregression as a top-performing and practical solution. Our approach is embodied in the Hierarchical Parallel Autoregressive ConvNet (HPAC), an ultra-lightweight pre-trained model using a hierarchical factorized structure and content-aware convolutional gating to efficiently capture spatial dependencies. We introduce two key optimizations for practicality: Cache-then-Select Inference (CSI), which accelerates coding by eliminating redundant computations, and Adaptive Focus Coding (AFC), which efficiently extends the framework to high bit-depth images. Building on this efficient foundation, our progressive adaptation strategy is realized by Spatially-Aware Rate-Guided Progressive Fine-tuning (SARP-FT). This instance-level strategy fine-tunes the model for each test image by optimizing low-rank adapters on progressively larger, spatially-continuous regions selected via estimated information density. Experiments on diverse datasets (natural, satellite, medical) validate that our method achieves new state-of-the-art compression. Notably, our approach sets a new benchmark in learned lossless compression, showing a carefully designed AR framework can offer significant gains over existing methods with a small parameter count and competitive coding speeds.