Despite years of research, real-time diverse grasp synthesis for dexterous hands remains an unsolved core challenge in robotics and computer graphics. We present Lightning Grasp, a novel high-performance procedural grasp synthesis algorithm that achieves orders-of-magnitude speedups over state-of-the-art approaches, while enabling unsupervised grasp generation for irregular, tool-like objects. The method avoids many limitations of prior approaches, such as the need for carefully tuned energy functions and sensitive initialization. This breakthrough is driven by a key insight: decoupling complex geometric computation from the search process via a simple, efficient data structure - the Contact Field. This abstraction collapses the problem complexity, enabling a procedural search at unprecedented speeds. We open-source our system to propel further innovation in robotic manipulation.