  Vortex lattice structures in Rashba noncentrosymmetric superconductors in
magnetic fields parallel to the basal plane (${\bf H} \perp c$) are examined
based on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional.
Due to the momentum dependent anisotropy of the Zeeman effect induced by the
broken inversion symmetry, the vortex lattice in higher fields generally shows
some unidirectional modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type
orienting in the plane perpendicular to ${\bf H}$. However, the direction of
the modulation and the lattice structure depend significantly on the underlying
pairing symmetry: When the mixing between spin singlet and triplet pairing
components is negligible, the resulting modulated structure tends to have
reflection symmetry, while the vortex lattice in systems with a significant
singlet-triplet mixing has no reflection symmetry in most cases. The latter
result implying the presence in {\it real} materials of two degenerate
orientations of the lattice structure separated by domain walls may be relevant
to the extremely low magnetic decay rate observed in CePt$_3$Si.
