Lattice paths are functional entities that model efficient navigation in discrete/grid maps. This paper presents a new scheme to generate collision-free lattice paths with utmost efficiency using the bijective property to rooted ordered trees, rendering a one-dimensional search problem. Our computational studies using ten state-of-the-art and relevant nature-inspired swarm heuristics in navigation scenarios with obstacles with convex and non-convex geometry show the practical feasibility and efficiency in rendering collision-free lattice paths. We believe our scheme may find use in devising fast algorithms for planning and combinatorial optimization in discrete maps.