  We analyse spatially resolved ALMA observations at 0.9, 1.3, and 3.1 mm for
the 26 brightest protoplanetary discs in the Lupus star-forming region. We
characterise the discs multi-wavelength brightness profiles by fitting the
interferometric visibilities in a homogeneous way, obtaining effective disc
sizes at the three wavelengths, spectral index profiles and optical depth
estimates. We report three fundamental discoveries: first, the millimeter
continuum size - luminosity relation already observed at 0.9 mm is also present
at 1.3 mm with an identical slope, and at 3.1 mm with a steeper slope,
confirming that emission at longer wavelengths becomes increasingly optically
thin. Second, when observed at 3.1 mm the discs appear to be only 9% smaller
than when observed at 0.9 mm, in tension with models of dust evolution which
predict a starker difference. Third, by forward modelling the sample of
measurements with a simple parametric disc model, we find that the presence of
large grains ($a_\mathrm{max}>1 $mm) throughout the discs is the most favoured
explanation for all discs as it reproduces simultaneously their spectral
indices, optical depth, luminosity, and radial extent in the 0.9-1.3 mm
wavelength range. We also find that the observations can be alternatively
interpreted with the discs being dominated by optically thick, unresolved,
substructures made of mm-sized grains with a high scattering albedo.
