  Using sound velocity and attenuation measurements in high magnetic fields, we
identify a new transition in the vortex lattice state of
La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO). The transition, observed in magnetic fields
exceeding 35 T and temperatures far below zero field $T_c$, is detected in the
compression modulus of the vortex lattice, at a doping level $x=p=0.17$. Our
theoretical analysis based on Eilenberger theory of vortex lattice shows that
the transition corresponds to the long-sought 45 degrees rotation of the square
vortex lattice, predicted to occur in $d$-wave superconductors near a van Hove
singularity.
