  We report small-angle neutron scattering measurements of the vortex lattice
(VL) structure in single crystals of the lightly underdoped cuprate
superconductor YBa2Cu3O6.85. At 2 K, and for fields of up to 16 T applied
parallel to the crystal c-axis, we observe a sequence of field-driven and
first-order transitions between different VL structures. By rotating the field
away from the c-axis, we observe each structure transition to shift to either
higher or lower field dependent on whether the field is rotated towards the
[100] or [010] direction. We use this latter observation to argue that the
Fermi surface morphology must play a key role in the mechanisms that drive the
VL structure transitions. Furthermore, we show this interpretation is
compatible with analogous results obtained previously on lightly overdoped
YBa2Cu3O7. In that material, it has long-been suggested that the high field VL
structure transition is driven by the nodal gap anisotropy. In contrast, the
results and discussion presented here bring into question the role, if any, of
a nodal gap anisotropy on the VL structure transitions in both YBa2Cu3O6.85 and
YBa2Cu3O7.
