We present a novel calculation of radiative corrections to the Lambda_b to Lambda_c form factors at large recoil up to next-to-leading logarithmic accuracy. Our calculation employs QCD light-cone sum rules and incorporates the Lambda_b-baryon distribution amplitudes, ensuring a comprehensive treatment of the scales. With adopting the diagrammatic approach, we establish the factorization formula for the vacuum-to-Lambda_b-baryon correlation function at LP and NLL supported by method of regions. Moreover, we present global fits of the form factors to our theoretical predictions at large recoil, simultaneously incorporating exclusive mesonic processes B^{*}_q to D^(*)_q and lattice QCD results, leading to significant advancements in the determination of the lepton-flavor-universality ratios R(Lambda_c).