This paper presents DD* Lite, an efficient incremental search algorithm for problems that can capitalize on state dominance. Dominance relationships between nodes are used to prune graphs in search algorithms. Thus, exploiting state dominance relationships can considerably speed up search problems in large state spaces, such as mobile robot path planning considering uncertainty, time, or energy constraints. Incremental search techniques are useful when changes can occur in the search graph, such as when re-planning paths for mobile robots in partially known environments. While algorithms such as D* and D* Lite are very efficient incremental search algorithms, they cannot be applied as formulated to search problems in which state dominance is used to prune the graph. DD* Lite extends D* Lite to seamlessly support reasoning about state dominance. It maintains the algorithmic simplicity and incremental search capability of D* Lite, while resulting in orders of magnitude increase in search efficiency in large state spaces with dominance. We illustrate the efficiency of DD* Lite with simulation results from applying the algorithm to a path planning problem with time and energy constraints. We also prove that DD* Lite is sound, complete, optimal, and efficient.