Stretching-dominated lattice materials are renowned for their lightweight nature and exceptional mechanical properties. These materials, however, have historically struggled with scalability towards low relative densities at which they often exhibit unstable oscillation behavior. Here, we propose a viable solution to this issue by integrating hollow truss elements and a grid distribution into the conventional octet truss lattice. The proposed grid hollow octet truss lattices demonstrate significant improvement over the conventional octet truss lattice, with stiffness and specific energy absorption capacities respectively 25.8% and 98% larger. To quantitatively assess the stability of low relative density metamaterials, three metrics are proposed and validated. The effect on the mechanical properties of the octet lattice of the ratio of inner to outer radius and of the grid number are comprehensively investigated numerically. Numerical simulations indicate that larger geometrical parameters and grid numbers significantly enhance the stability of the octet lattice. Consequently, the proposed lattices exhibit comparable energy absorption capacity as smooth shell lattices at equivalent relative density but demonstrate a more stable nonlinear response, maintaining nearly constant stress levels at a relative density of 0.1. Experimental validation supports these findings, highlighting potential for applications to load bearing and energy absorption.