No transient electromagnetic emission has yet been found in association to fast radio bursts ( FRBs ) , the only possible exception ( 3 \sigma 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 FRB 131104 . 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 , FRB 010724 ( 800 \pm 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 FRB 131104 and found no significant emission down to a 5 \sigma limit in the range ( 0.24 – 4.7 ) \times 10 ^ { -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 FRB 131104 . 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 \pm 3 pc cm ^ { -3 } ) and an inferred redshift limit of z < 0.4 .