  We present new 890 $\mu m$ continuum ALMA observations of 5 brown dwarfs
(BDs) with infrared excess in Lupus I and III -- which, in combination with 4
BDs previously observed, allowed us to study the mm properties of the full
known BD disk population of one star-forming region. Emission is detected in 5
out of the 9 BD disks. Dust disk mass, brightness profiles and characteristic
sizes of the BD population are inferred from continuum flux and modeling of the
observations. Only one source is marginally resolved, allowing for the
determination of its disk characteristic size. We conduct a demographic
comparison between the properties of disks around BDs and stars in Lupus. Due
to the small sample size, we cannot confirm or disprove if the disk mass over
stellar mass ratio drops for BDs, as suggested for Ophiuchus. Nevertheless, we
find that all detected BD disks have an estimated dust mass between 0.2 and 3.2
$M_{\bigoplus}$; these results suggest that the measured solid masses in BD
disks can not explain the observed exoplanet population, analogous to earlier
findings on disks around more massive stars. Combined with the low estimated
accretion rates, and assuming that the mm-continuum emission is a reliable
proxy for the total disk mass, we derive ratios of $\dot{M}_{\mathrm{acc}} /
M_{\mathrm{disk}}$ significantly lower than in disks around more massive stars.
If confirmed with more accurate measurements of disk gas masses, this result
could imply a qualitatively different relationship between disk masses and
inward gas transport in BD disks.
