  Elastic neutrino-electron scattering represents a powerful tool to
investigate key neutrino properties. In view of the recent results released by
the LUX-ZEPLIN collaboration, we provide a first determination of the limits
achievable on the neutrino magnetic moment and neutrino millicharge, whose
effect becomes non-negligible in some beyond the Standard Model theories. In
this context, we evaluate and discuss the impact of different approximations to
describe the neutrino interaction with atomic electrons. The new LUX-ZEPLIN
data allows us to set a very competitive limit on the neutrino magnetic moment
when compared to the other laboratory bounds, namely $\mu_{\nu}^{\rm{eff}} <
1.1 \times 10^{-11} \, \mu_{\text{B}}$ at 90$\%$ C.L., which improves by a
factor of 2.5 the Borexino collaboration limit and represents the second best
world limit after the recent XENONnT result. Moreover, exploiting the so-called
equivalent photon approximation, we obtain the most stringent limit on the
neutrino millicharge, namely $|q_{\nu}^{\rm{eff}}| < 1.5 \times 10^{-13} e_0$
at 90$\%$ C.L., which represents a great improvement with respect to the
previous laboratory bounds.
