This paper studies the static mechanical properties of four-sided concave pyramid-type lattice structures with a polyurea coating and a negative Poisson's ratio. Experimental models of different types were made by the additive manufacturing method. Quasi-static compression experiments of lattice structures, and three-point and four-point bending experiments of lattice sandwich structures, were implemented. The lattice structure exhibited a significantly negative Poisson's ratio effect under compressive load. Under platform stresses of 0.6-1.0 MPa, the polyurea coating obviously improved the mechanical properties of the lattice structures. The total energy absorption, deformation energy per unit volume, and specific energy absorption were significantly higher (by 1-2 orders of magnitude) in the multicellular polyurea-coated models than in the uncoated models. The maximum energy-absorption efficiency and compression utilization in the polyurea-coated models reached 40.59% and 55.15%, respectively. In the lattice structures without polyurea, the deformation energy per unit volume, specific energy absorption, maximum energy-absorption efficiency, and compression utilization decreased with increasing number of units. These trends are attributable to early brittle fracture. Meanwhile, the energy-absorption characteristics of the polyurea-coated lattice structures largely depended on the polyurea thickness. Under a bending load, the polyurea-uncoated lattice sandwich structures were prone to partial core collapse, especially around the indenter. The destruction degree reduced layer by layer outward to the core. The upper and lower panels showed fold-line deformation and a curved deformation mode, respectively. The upper panel developed a "U-shaped" deformation mode at an early stage, and its core failure range was widely reduced. The lower panel was 19.61%-42.03% more deformed in the polyurea-coated than in the uncoated lattice sandwich structures. The results provide a reference for the design of lightweight and efficient energy-absorptive structures for ship protection.