We present a multi-wavelength analysis of 48 submillimeter galaxies (SMGs) detected in the LABOCA/ACT Survey of Clusters at All Redshifts, LASCAR, which acquired new 870 $mu$m and ATCA 2.1 GHz observations of ten galaxy clusters detected through their Sunyaev-Zeldovich effect (SZE) signal by the Atacama Cosmology Telescope. Far-infrared observations were also conducted with the PACS (100/160 $mu$m) and SPIRE (250/350/500 $mu$m) instruments on $Herschel$ for sample subsets of five and six clusters. LASCAR 870 $mu$m, maps were reduced using a multi-scale iterative pipeline that removes the SZE increment signal, yielding point-source sensitivities of $sigmasim2rm{,mJy,beam}^{-1}$. We detect in total 49 sources at the $4sigma$ level, and conduct a detailed multi-wavelength analysis considering our new radio and far-IR observations plus existing near-IR and optical data. One source is identified as a foreground galaxy, 28 SMGs are matched to single radio sources, 4 have double radio counterparts, and 16 are undetected at 2.1 GHz but tentatively associated in some cases to near-IR/optical sources. We estimate photometric redshifts for 34 sources with secure (25) and tentative (9) matches at different wavelengths, obtaining a median $z=2.8^{+2.1}_{-1.7}$. Compared to previous results for single-dish surveys, our redshift distribution has a comparatively larger fraction of sources at $z>3$ and the high-redshift tail is more extended. This is consistent with millimeter spectroscopic confirmation of a growing number of high-$z$ SMGs and relevant for testing of cosmological models. Analytical lens modeling is applied to estimate magnification factors for 42 SMGs at cluster-centric radii $>1.2$; with the demagnified flux densities and source-plane areas, we obtain integral number counts that agree with previous submillimeter surveys.
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