As long as the external magnetic field does not destroy the Cooper pair of electrons, this pair does not experience the Lorentz force.
Not only charged particles, when moved through a not parallel to the movement magnetic field, get deflected, but also neutrons get deflected. This happens for all particles and also for atoms and molecules, if their summarized magnetic dipole moment is not zero.
The magnetic dipole moment of each involved proton, electron and neutron is connected to an intrinsic spin. As has been shown by the Einstein-de-Haas experiment (not a thought experiment, but really carried out), the intrinsic spin has to do with spinning around an axis and this spin is pointing in the same direction as the magnetic dipole moment (has the same axis).
In analogy to a gyroscope, the intrinsic spin resists against deflection from a straight line. The result is a precession: When an external force try to change the direction of the axis of a gyroscope, the spin axis does not follow the direction of this force, but get deflected from a right angle to it.
But this holds only if the intrinsic spins of the involved constituents does not cancels out. An example for not canceling out spins is the Stern-Gerlach experiment. Cooper pairs are the perfect example for a spin sum equal to zero. How the repelling electric forces do not destroy the Cooper pair is another question.