The physics behind the rhombic-->square-->rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi2B2C is due to intrinsic competition between the superconducting gap and Fermi surface anisotropies. The calculations not only reproduce it but also predict the not yet found lock-in transition to a square lattice with different orientation in a higher field. In view of the physical origin given, this sequence of transitions is rather generic to occur in fourfold symmetric superconductors.