  We introduce a general and accurate method for determining lattice phase
shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices.
Our method combines angular momentum projection, spherical wall boundaries and
an adjustable auxiliary potential. This allows us to construct radial lattice
wave functions and to determine phase shifts at arbitrary energies. For coupled
partial waves, we use a complex-valued auxiliary potential that breaks
time-reversal invariance. We benchmark our method using a system of two
spin-1/2 particles interacting through a finite-range potential with a strong
tensor component. We are able to extract phase shifts and mixing angles for all
angular momenta and energies, with precision greater than that of extant
methods. We discuss a wide range of applications from nuclear lattice
simulations to optical lattice experiments.
