  Lions (1959, Bull. Soc. Math. France, \textbf{87}, 245--273) introduced the
Navier-Stokes equations with a viscous diffusion in the form of a fractional
Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the
uniqueness of its solution when its exponent is not less than five quarters in
case the spatial dimension is three. Following the work of
Hofmanov$\acute{\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]),
we prove the non-uniqueness in law for the three-dimensional stochastic
Navier-Stokes equations with the viscous diffusion in the form of a fractional
Laplacian with its exponent less than five quarters.
