  The anisotropy of the nuclear spin-lattice relaxation rate $1/T_{1}$ of
$^{75}$As was investigated in the iron-based superconductor
LaFeAs(O$_{1-x}$F$_{x}$) ($x = 0.07, 0.11$ and 0.14) as well as LaFeAsO. While
the temperature dependence of the normal-state $1/T_1T$ in the superconducting
(SC) $x = 0.07$ is different from that in the SC $x = 0.11$, their anisotropy
of $1/T_1$, $R \equiv (1/T_{1})_{H \parallel ab}/(1/T_{1})_{H \parallel c}$ in
the normal state is almost the same ($\simeq$ 1.5). The observed anisotropy is
ascribable to the presence of the local stripe correlations with $Q = (\pi, 0)$
or $(0, \pi)$. In contrast, $1/T_1$ is isotropic and $R$ is approximately 1 in
the overdoped $x = 0.14$ sample, where superconductivity is almost suppressed.
These results suggest that the presence of the local stripe correlations
originating from the nesting between hole and electron Fermi surfaces is linked
to high-$T_c$ superconductivity in iron pnictides.
