1961 method: flood outward from the start pin cell by cell until you hit the target, then trace back. Always finds a path if one exists; slow on big boards.
How it looks
Drawing: a routing grid, not a part of CORE3588
Lee's method is a procedure, not a physical object, so this is a drawing: the finished ripple (numbers = steps from A, 83 squares filled) and the shortest path it found (amber). A real router does the same on a grid of tens of thousands of squares per layer, about 0.025 to 0.1 mm each (a lattice).
How it works
Where it fits
Lee is the oldest way to find one path for one connection. A* search finds the same path while looking at far fewer squares, and a cost function lets the path prefer fewer vias or bends, not only fewer steps.