Recent observations with the GISMO (Goddard-IRAM Superconducting 2 Millimeter Observer) 2mm camera revealed a detection 8arcsec away from the lensed galaxy MACS1149-JD1 at z=9.6. Within the 17.5arcsec FWHM GISMO beam, this detection is consistent with the position of the high-redshift galaxy and therefore, if confirmed, this object could be claimed to be the youngest galaxy producing significant quantities of dust. We present higher resolution (8.5arcsec) observations of this system taken with the AzTEC 1.1mm camera mounted on the Large Millimeter Telescope Alfonso Serrano. Dust continuum emission at the position of MACS1149-JD1 is not detected with an r.m.s. of 0.17 mJy/beam. However, we find a detection ~11arcsec away from MACS1149-JD1, still within the GISMO beam which is consistent with an association to the GISMO source. Combining the AzTEC and GISMO photometry, together with Herschel ancillary data, we derive a zphot=0.7-1.6 for the dusty galaxy. We conclude therefore that the GISMO and AzTEC detections are not associated with MACS1149-JD1. From the non-detection of MACS1149-JD1 we derive the following (3σ) upper limits corrected for gravitational lensing magnification and for cosmic microwave background effects: dust mass <1.6x107 M⊙, IR luminosity <8x1010 L⊙, star formation rate <14M⊙yr-1, and UV attenuation <2.7mag. These limits are comparable to those derived for other high-redshift galaxies from deep Atacama Large Millimeter/submillimeter Array observations.