We present Scanning Tunneling Microscope (STM) observations of the sup
erconducting energy gap and vortex lattice (VL) structure of the (001)
face of a LuNi2B2C single crystal. In zero held, the conductance vers
us voltage characteristics consistently show a peaked structure that c
an be fitted with a broadened BCS Like density of states, giving a gap
value of 2.2 meV and 2 Delta/kT(c) = 3.2 +/- 0.1, implying weak coupl
ing superconductivity. In applied magnetic fields of 0.375 T and 1.5 T
, we make the first STM observation of a square VL, with its unit cell
rotated 45 degrees with respect to the crystallographic unit cell. Th
e VL structure is analyzed with Ginzburg-Landau theory, including an a
dditional free energy term with four-fold symmetry arising from the te
tragonal crystal structure. The square VL is found to be stable if the
four-fold free energy term is large enough to cause the ratio of the
in-plane upper critical fields H-c2 (45 degrees)/H-c2 (0) to be less t
han 0.97. Measurements of the in-plane upper critical field anisotropy
by SQUID magnetometry show a ratio of 0.92 at 4.2 K, consistent with
the Ginzburg-Landau analysis.