  The gravitationally lensed Lyman-alpha emitting galaxy, HCM6A, detected by Hu
et al. (2002) at z=6.56 behind the Abell 370 cluster was observed with the
MAMBO-2 array of bolometers at 1.2mm wavelength. The galaxy was not detected
down to 1.08 mJy (3 sigma), but the depth of the observations and the lens
amplification allow us to improve by approximately one order of magnitude
previously published upper limits on far infrared emission of Lyman-alpha
emitting galaxies at this redshift. The following upper limits are derived from
our observations assuming typical dust parameters: dust mass <5.3x10^7 Msun, IR
luminosity <2.1x10^{11} Lsun, and star formation rate, SFR<35 Msun/yr. The
observed restframe UV--optical--IR spectral energy distribution (SED) of this
galaxy is compatible with that of normal spiral galaxies or blue compact dwarf
galaxies. SEDs of prototypical ULIRGs, such as Arp 220, are clearly excluded.
Finally, we obtain an upper limit of < 2.1x10^{-2} Msun/yr/Mpc^{-3} for the
dust-obscured SFR density of Lyman-alpha selected galaxies at z~6.6.
