Additive manufacturing is a disruptive technology that can be leveraged by the redesign of components in most engineering fields. Fundamental engineering resources for lightweight mirrors were developed more than 30 years ago with a main design limitation, state of the art manufacturing. Here, we present two design methodologies for the design of lightweight mirrors. The first method utilizes analytical expressions to design a traditional isogrid mirror, which provided the foundation for most lightweight mirrors to date. The second method employs a combination of topology optimization, lattice infill, and analytical estimation to develop an advanced lightweight mirror designed for additive manufacturing. The advanced mirror design outperforms the traditional design for each functional requirement, including a 94% reduction in predicted surface quilting and a higher specific stiffness. The manufacturing of the advanced mirror is only possible with an additive manufacturing process.