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We present a lazy incremental search algorithm, Lifelong-GLS (L-GLS), along with its bounded suboptimal version, Bounded L-GLS (B-LGLS) that combine the search efficiency of incremental search algorithms with the evaluation efficiency of lazy search algorithms for fast replanning in problem domains where edge evaluations are more expensive than vertex expansions. The proposed algorithms generalize Lifelong Planning A* (LPA*) and its bounded suboptimal version, Truncated LPA* (TLPA*), within the Generalized Lazy Search (GLS) framework, so as to restrict expensive edge evaluations only to the current shortest subpath when the cost-to-come inconsistencies are propagated during repair. We also present dynamic versions of the L-GLS and B-LGLS algorithms, called Generalized D* (GD*) and Bounded Generalized D* (B-GD*), respectively, for efficient replanning with non-stationary queries, designed specifically for navigation of mobile robots. We prove that the proposed algorithms are complete and correct in finding a solution that is guaranteed not to exceed the optimal solution cost by a user-chosen factor. Our numerical and experimental results support the claim that the proposed integration of the incremental and lazy search frameworks can help find solutions faster compared to the regular incremental or regular lazy search algorithms when the underlying graph representation changes often.