This paper considers the general lot sizing and scheduling problem with rich constraints exemplified by means of rework and lifetime constraints for defective items (GLSP-RP), which finds numerous applications in industrial settings, for example, the food processing industry and the pharmaceutical industry. To address this problem, we propose the Late Acceptance Hill-climbing Matheuristic (LAHCM) as a novel solution framework that exploits and integrates the late acceptance hill climbing algorithm and exact approaches for speeding up the solution process in comparison to solving the problem by means of a general solver. The computational results show the benefits of incorporating exact approaches within the LAHCM template leading to high-quality solutions within short computational times.