  We present the results of a blind millimeter line emitter search using ALMA
Band 6 data with a single frequency tuning toward four gravitational lensing
clusters (RXJ1347.5-1145, Abell S0592, MACS J0416.1-2403, and Abell 2744). We
construct three-dimensional signal-to-noise ratio (S/N) cubes with 60 MHz and
100 MHz binning, and search for millimeter line emitters. We do not detect any
line emitters with a peak S/N > 5, although we do find a line emitter candidate
with a peak S/N ~ 4.5. These results provide upper limits to the CO(3-2),
CO(4-3), CO(5-4), and [CII] luminosity functions at z ~ 0.3, 0.7, 1.2, and 6,
respectively. Because of the magnification effect of gravitational lensing
clusters, the new data provide the first constraints on the CO and [CII]
luminosity functions at unprecedentedly low luminosity levels, i.e., down to
$<~ 10^{-3}-10^{-1} $Mpc$^{-3}$ dex$^{-1}$ at $L'_{CO} ~ 10^8-10^{10}$ K km
$s^{-1}$ pc$^2$ and $<~ 10^{-3}-10^{-2}$ Mpc$^{-3}$ dex$^{-1}$ at $L_[CII] ~
10^8-10^{10} L_\odot$, respectively. Although the constraints to date are not
stringent yet, we find that the evolution of the CO and [CII] luminosity
functions are broadly consistent with the predictions of semi-analytical
models. This study demonstrates that the wide observations with a single
frequency tuning toward gravitational lensing clusters are promising for
constraining the CO and [CII] luminosity functions.
