  The spin lifetime anisotropy is an important quantity for investigating the
spin relaxation mechanisms in graphene and in heterostructures of
two-dimensional materials. We generalize the diffusive spin transport equations
of oblique spin precession in a lateral spin valve with finite contact
resistance. This yields a method to determine the spin lifetime anisotropy
ratio {\xi}={\tau}$_{\perp}$/{\tau}$_{\parallel}$, which is the ratio between
lifetimes of spin polarized perpendicular and parallel to the graphene surface.
By solving the steady-state Bloch equations, we show that the line-shape of the
oblique spin precession signal can be described with six dimensionless
parameters, which can be solved analytically. We demonstrate that the
anisotropic spin precession characteristics can be strongly suppressed by
contact induced spin relaxation originating from conductance mismatch between
the channel material and electrodes. To extract the spin lifetime anisotropy
ratio accurately, we develop a closed form equation that includes the effect of
finite contact resistance. Furthermore, we demonstrate that in the high contact
resistance regime, the minimum channel length required for accurately
determining the spin lifetime anisotropy for a sufficiently low external
magnetic field is only determined by the diffusion coefficient of the channel
material, as opposed to the spin diffusion length. Our work provides an
accurate model to extract the spin lifetime anisotropy ratio from the oblique
spin precession measurement, and can be used to guide the device design for
such measurements.
