We use small-angle neutron scattering to study the superconducting vortex lattice in La2−xSrxCuO4 as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length ξ are controlled by a Van Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that spin-density-wave order acts as a source of disorder on the vortex lattice.