We present observations aimed at exploring both the nature of Lya emitting nebulae (Lya blobs) at z=2.38 and the way they trace large scale structure (LSS), by exploring their proximity to maximum starbursts through submillimeter emission. Our most important objectives are to make a census of associated submillimeter galaxies (SMGs), check their properties, and look for a possible overdensity in the protocluster J2142-4426 at z=2.38. We used the newly commissioned Large APEX Bolometer Camera (LABoCa) on the Atacama Pathfinder EXperiment (APEX) telescope, in its Science Verification phase, to carry out a deep 10x10 map at 870 micron, and we performed multiple checks of the quality of data processing and source extraction. Our map, the first published deep image, confirms the capabilities of APEX/LABoCa as the most efficient current equipment for wide and deep submm mapping. Twenty-two sources were securely extracted with 870 micron flux densities in the range 3-21 mJy, rms noise 0.8-2.4 mJy, and far-IR luminosities probably in the range ~5-20 x 10(12) Lo. Only one of the four 50 kpc-extended Lya blobs has a secure 870 micron counterpart. The 870 micron source counts in the whole area are marginally higher than in the SHADES SCUBA survey, with a possible over-density around this blob. The majority of the 3.6-24 micron SEDs of the submillimeter sources indicate they are starburst dominated, with redshifts mostly >2. However, there is evidence of a high-z AGN in ~30% of the sources.
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