  The dominant mechanism leading to the formation of brown dwarfs (BDs) remains
uncertain. The most direct keys to formation, which are obtained from younger
objects (pre-BD cores and proto-BDs), are limited by the very low number
statistics available. We aim to identify and characterize a set of pre- and
proto-BDs as well as Class II BDs in the Lupus 1 and 3 molecular clouds to test
their formation mechanism. We performed ALMA band 6 (1.3 mm) continuum
observations of a selection of 64 cores previously identified from AzTEC/ASTE
data (1.1 mm), along with previously known Class II BDs in the Lupus 1 and 3
molecular clouds. Surveyed archival data in the optical were used to complement
these observations. We expect these ALMA observations prove efficient in
detecting the youngest sources in these regions, since they probe the frequency
domain at which these sources emit most of their radiation. We detected 19
sources from 15 ALMA fields. Considering all the pointings in our observing
setup, the ALMA detection rate was $\sim$23% and the derived masses of the
detected sources were between $\sim$0.18 and 124 $\mathrm{M_{Jup}}$. We
classified these sources according to their spectral energy distribution as 5
Class II sources, 2 new Class I/0 candidats, and 12 new possible pre-BD or
deeply embedded protostellar candidates. We detected a promising candidate for
a Class 0/I proto-BD source and inferred the disk dust mass of a bona fide
Class II BD. The pre-BD cores might be the byproduct of an ongoing process of
large-scale collapse. The Class II BD disks follow the correlation between disk
mass and the mass of the central object that is observed at the low-mass
stellar regime. We conclude that it is highly probable that the sources in the
sample are formed as a scaled-down version of low-mass star formation, although
disk fragmentation may be responsible for a considerable fraction of BDs.
