The tree-level b -> cl (v) over bar (l) based hadronic transitions have been the focus of much attention since recording significant deviations of the experimental data, on the ratios of the branching fractions in tau and e - mu channels of the semileptonic B -> D transition, from the SM predictions by the BABAR Collaboration in 2012. It can be of great importance to look whether similar discrepancies take place in the semileptonic baryonic Lambda(b) -> Lambda(c)l (v) over bar (l) decay channel or not. In this accordance we estimate the decay width as well as the ratios of the branching fractions in tau and e - mu channels of this baryonic transition by calculating the form factors, entering the amplitude of this transition as the main inputs, in the framework of QCD sum rules in full theory. We compare the obtained results with the predictions of other theoretical studies. Our results may be compared with the corresponding future experimental data to look for possible deviations of data from the SM predictions.