Lossless image compression is required in various applications to reduce storage or transmission costs of images, while requiring the reconstructed images to have zero information loss compared to the original. Existing lossless image compression methods either have simple design but poor compression performance, or complex design, better performance, but with no performance guarantees. In our endeavor to develop a lossless image compression method with low complexity and guaranteed performance, we argue that compressibility of a color image is essentially derived from the patterns in its spatial structure, intensity variations, and color variations. Thus, we divide the overall design of a lossless image compression scheme into three parts that exploit corresponding redundancies. We further argue that the binarized version of an image captures its fundamental spatial structure. In this first part of our work, we propose a scheme for lossless compression of binary images. The proposed scheme first learns dictionaries of $16\times16$, $8\times8$, $4\times4$, and $2\times 2$ square pixel patterns from various datasets of binary images. It then uses these dictionaries to encode binary images. These dictionaries have various interesting properties that are further exploited to construct an efficient and scalable scheme. Our preliminary results show that the proposed scheme consistently outperforms existing conventional and learning based lossless compression approaches, and provides, on average, as much as $1.5\times$ better performance than a common general purpose lossless compression scheme (WebP), more than $3\times$ better performance than a state of the art learning based scheme, and better performance than a specialized scheme for binary image compression (JBIG2).