The low-pressure phase diagram of La${}_3$Ni${}_2$O${}_7$ provides an important reference for understanding its pressure-induced high-temperature superconductivity. While the spin-density-wave transition at $T_{\mathrm{\text{SDW}}}\approx 150$ K is increasingly well established, the origin of the second density-wave transition at $T_{\mathrm{\text{DW}}}\approx 130$ K has remained unresolved. Here, we perform unrestricted Hartree–Fock calculations to investigate the potential origin of the second transition. Within the orthorhombic phase, the degeneracy between possible ordering wavevectors at ${𝐐}_Y=(0,\pi )$ and at ${𝐐}_X=(\pi ,0)$ is lifted and the electronic system develops a double-stripe spin-density wave with ordering vector ${𝐐}_Y=(0,\pi )$. We identify that the pure double stripe spin state is unstable in La${}_3$Ni${}_2$O${}_7$ towards a commensurate charge-density wave instability, which favors a spin-modulated double stripe order with intertwined charge and spin instabilities and establish the hierarchy of ordered states in La${}_3$Ni${}_2$O${}_7$. We further discuss our results in the context of available experimental literature and propose further experimental tests to elucidate the origin of the SDW/DW states in this system.