  The physics behind the rhombic$\to$square$\to$rhombic flux line lattice
transformation in increasing fields is clarified on the basis of Eilenberger
theory. We demonstrate that this reentrance observed in LuNi$_2$B$_2$C is due
to intrinsic competition between superconducting gap and Fermi surface
anisotropies. The calculations reproduce not only it but also predict yet not
found lock-in transition to a square lattice with different orientation in
higher field. In view of physical origin given, this sequence of transitions is
rather generic to occur in four-fold symmetric superconductors.
