  Inelastic spin relaxation and spin splitting $\epsilon_{\mathrm{s}}$ in
lateral quantum dots are studied in the regime of strong in-plane magnetic
field. Due to both g-factor energy dependence and spin-orbit coupling
$\epsilon_{\mathrm{s}}$ demonstrates a substantial non-linear magnetic field
dependence similar to that observed by R.Hanson \textit{et al} [Phys. Rev.
Lett. \textbf{91}, 196802 (2003)]. It also varies with the in-plane orientation
of magnetic field due to crystalline anisotropy of spin-orbit coupling. Spin
relaxation rate is also anisotropic, the anisotropy increasing with the field.
When the magnetic length is less than the 'thickness' of GaAs dot, the
relaxation can be order of magnitude faster for $\mathbf{B}% \Vert\lbrack100]$
than for $\mathbf{B\Vert}[110]$.
