  We use accurate ab initio and quantum scattering calculations to explore the
prospects for sympathetic cooling of the heavy molecular radical
SrOH($^2\Sigma$) by ultracold Li atoms in a magnetic trap. A two-dimensional
potential energy surface (PES) for the triplet electronic state of Li-SrOH is
calculated ab initio using the partially spin-restricted coupled cluster method
with single, double and perturbative triple excitations and a large
correlation-consistent basis set. The highly anisotropic PES has a deep global
minimum in the skewed Li-HOSr geometry with $D_e=4932$ cm$^{-1}$ and saddle
points in collinear configurations. Our quantum scattering calculations predict
low spin relaxation rates in fully spin-polarized Li+SrOH collisions with the
ratios of elastic to inelastic collision rates well in excess of 100 over a
wide range of magnetic fields (1-1000 G) and collision energies
(10$^{-5}-0.1$~K) suggesting favorable prospects for sympathetic cooling of
SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that
spin relaxation in Li+SrOH collisions occurs via a direct mechanism mediated by
the magnetic dipole-dipole interaction between the electron spins of Li and
SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed.
The upper limit to the Li+SrOH reaction rate coefficient calculated for the
singlet PES using adiabatic capture theory is found to decrease from $4\times
10^{-10}$~cm$^3$/s to a limiting value of $3.5\times 10^{-10}$ cm$^3$/s with
decreasing temperature from 0.1 K to 1 $\mu$K.
