Lattice metamaterials emerge as advanced architected materials with superior physical properties and significant potential for lightweight applications. Recent developments in additive manufacturing (AM) techniques facilitate the manufacturing of lattice metamaterials with intricate microarchitectures and promote their applications in multi-physical scenarios. Previous reviews on lattice metamaterials have largely focused on a specific/single physical field, with limited discussion on their multi-physical properties, interaction mechanisms, and multifunctional applications. Accordingly, this article critically reviews the design principles, structure-mechanism-property relationships, interaction mechanisms, and multifunctional applications of multi-physical lattice metamaterials enabled by AM techniques. First, lattice metamaterials are categorized into homogeneous lattices, inhomogeneous lattices, and other forms, whose design principles and AM processes are critically discussed, including the benefits and drawbacks of different AM techniques for fabricating different types of lattices. Subsequently, the structure-mechanism-property relationships and interaction mechanisms of lattice metamaterials in a range of physical fields, including mechanical, acoustic, electromagnetic/optical, and thermal disciplines, are summarized to reveal critical design principles. Moreover, the multifunctional applications of lattice metamaterials, such as sound absorbers, insulators, and manipulators, sensors, actuators, and soft robots, thermal management, invisible cloaks, and biomedical implants, are enumerated. These design principles and structure-mechanism-property relationships provide effective design guidelines for lattice metamaterials in multifunctional applications.