Non-stochastic lattice structures are patterned after the unit cell topology and are of interest to the research and design communities for improving stiffness to weight ratios and/or metamaterial design. While additive manufacturing (AM) increases design freedom, it remains difficult to design or select an appropriate unit cell topology. In this work, a ground structure topology optimization approach is developed for unit cell design. Using a multi-objective evolutionary algorithm, this framework incorporates a library of different objectives, constraints, and penalties. The Additive Lattice Topology Optimization (ALTO) approach generates novel lattice structures for AM from the selected design objectives. A key purpose of this framework is incorporating AM process considerations into the optimization through objectives, constraints, and penalty functions for improved manufacturability. Two case studies presented in this work demonstrate ALTO's ability to generate novel lattice structures with specific functionality while accounting for AM process constraints for laser powder bed fusion. Case Study 1 is an example of generating a lattice structure for heat sink applications. Case Study 2 demonstrates creation of three novel lattices with different stiffness properties, each with the same volume fraction. Using ground structure topology optimization and incorporating AM process considerations, ALTO is a unique approach for improved lattice structure design.