We have studied the filaments extracted from the column density maps of the nearby Lupus 1, 3, and 4 molecular clouds, derived from photometric maps observed with the Herschel satellite. Filaments in the Lupus clouds have quite low column densities, with a median value of $\sim$1.5$\times$10$^{21}$ cm$^{-2}$ and most have masses per unit length lower than the maximum critical value for radial gravitational collapse. Indeed, no evidence of filament contraction has been seen in the gas kinematics. We find that some filaments, that on average are thermally subcritical, contain dense cores that may eventually form stars. This is an indication that in the low column density regime, the critical condition for the formation of stars may be reached only locally and this condition is not a global property of the filament. Finally, in Lupus we find multiple observational evidences of the key role that the magnetic field plays in forming filaments, and determining their confinement and dynamical evolution.

16 pages, 16 figures