  Generation of arbitrarily spin-polarized lepton (here refer in particular to
electron and positron) beams has been investigated in the single-shot
interaction of high-energy polarized $\gamma$ photons with an ultraintense
asymmetric laser pulse via nonlinear Breit-Wheeler (BW) pair production. We
develop a fully spin-resolved semi-classical Monte Carlo method to describe the
pair creation and polarization in the local constant field approximation. In
nonlinear BW process the polarization of created pairs is simultaneously
determined by the polarization of parent $\gamma$ photons, the polarization and
asymmetry of scattering laser field, due to the spin angular momentum transfer
and the asymmetric spin-dependent pair production probabilities, respectively.
In considered all-optical method, dense GeV lepton beams with average
polarization degree up to about $80\%$ (adjustable between the transverse and
longitudinal components) can be obtained with currently achievable laser
facilities, which could be used as injectors of the polarized $e^{+}e^{-}$
collider to search for new physics beyond the Standard Model.
