© 2022 authors. Published by the American Physical Society.The weak decays of doubly heavy ΞQQ baryon induced by flavor changing b→d and c→u flavor changing neutral current within the light-cone sum rules are studied. The sum rules are constructed and analyzed for the corresponding transition form factors using the parallel components of the light-cone distribution amplitudes for ΛQ baryon. Having the results for the form factors, the corresponding branching ratios for ΞQQ→ΛQl+l- decays are estimated. While the branching ratio due to b→d transition is around 10-9, in c→u transition case, it is found as around 10-13. Hence, Ξbb→Λbl+l- decay has the potential of being discovered at LHCb. However, Ξbb→Λbl+l- is difficult to be measured due to the extremely small values of obtained branching ratio. Our results on the branching ratio are also compared with the results of the light-front approach.