  We utilize a combination of vector magnetic field and scanning tunneling
microscopy to elucidate the 3D field-based electronic phase diagram of a
correlated iron-based superconductor, LiFeAs. We observe, under a
zero-field-cooled method, an ordered hexagonal vortex lattice ground-state in
contrast to the disordered lattice observed under a field-cooled method. It
transforms into a four-fold-symmetric state by increasing c-axis field and
distorts elliptically upon tilting the field in-plane. The vortex lattice
transformations correlate with the field dependent superconducting gap that
characterizes the Cooper pairing strength. The anisotropy of the vortex lattice
agrees with the field enhanced Bogoliubov quasiparticle scattering channel that
is determined by the pairing symmetry with respect to its Fermi surface
structure. Our systematic tuning of the vortex lattice symmetry and study of
its correlation with Cooper pairing demonstrates the many-body interplay
between the superconducting order parameter and emergent vortex matter.
