No transient electromagnetic emission has yet been found in association to fast radio bursts (FRBs), the only possible exception (3sigma confidence) being the putative gamma-ray signal detected in Swift/BAT data in the energy band 15-150 keV at the time and position of FRB131104. Systematic searches for hard X/gamma-ray counterparts to other FRBs ended up with just lower limits on the radio/gamma-ray fluence ratios. In 2001, at the time of the earliest discovered FRBs, the BeppoSAX Gamma-Ray Burst Monitor (GRBM) was one of the most sensitive open sky gamma-ray monitors in the 40-700~keV energy band. During its lifetime, one of the FRBs with the highest radio fluence ever recorded, FRB010724 (800 +- 400 Jy ms), also known as the Lorimer burst, was promptly visible to the GRBM. Upon an accurate modeling of the GRBM background, eased by its equatorial orbit, we searched for a possible gamma-ray signal in the first 400 s following the FRB, similar to that claimed for FRB131104 and found no significant emission down to a 5-sigma limit in the range (0.24-4.7)x10^-6 erg cm^-2 (corresponding to 1 and 400 s integration time, respectively), in the energy band 40-700 keV. This corresponds to eta = F_radio/F_gamma>10^{8-9} Jy ms erg^-1 cm^2, i.e. the deepest limit on the ratio between radio and gamma-ray fluence, which rules out a gamma-ray counterpart similar to that of FRB131104. We discuss the implications on the possible mechanisms and progenitors that have been proposed in the literature, also taking into account its relatively low dispersion measure (375 +- 3 pc cm^-3) and an inferred redshift limit of z<0.4.
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