  We present the first ALMA survey of protoplanetary discs at 3 mm, targeting
36 young stellar objects in the Lupus star-forming region with deep
observations (sensitivity 20-50 microJy/beam) at ~0.35" resolution (~50 au).
Building on previous ALMA surveys at 0.89 and 1.3 mm that observed the complete
sample of Class II discs in Lupus at a comparable resolution, we aim to assess
the level of grain growth in the relatively young Lupus region. We measure 3 mm
integrated fluxes, from which we derive disc-averaged 1-3 mm spectral indices.
We find that the mean spectral index of the observed Lupus discs is
$\alpha_\mathrm{1-3 mm}=2.23\pm0.06$, in all cases $\alpha_\mathrm{1-3
mm}<3.0$, with a tendency for larger spectral indices in the brightest discs
and in transition discs. Furthermore, we find that the distribution of spectral
indices in Lupus discs is statistically indistinguishable from that of the
Taurus and Ophiuchus star-forming regions. Assuming the emission is optically
thin, the low values $\alpha_\mathrm{1-3 mm}\leq 2.5$ measured for most discs
can be interpreted with the presence of grains larger than 1 mm. The
observations of the faint discs in the sample can be explained without invoking
the presence of large grains, namely through a mixture of optically thin and
optically thick emission from small grains. However, the bright (and typically
large) discs do inescapably require the presence of millimeter-sized grains in
order to have realistic masses. Based on a disc mass argument, our results
challenge previous claims that the presence of optically thick sub-structures
may be a universal explanation for the empirical millimeter size-luminosity
correlation observed at 0.89 mm.
