Taking into account the Lambda baryon distribution amplitudes and the most general form of the interpolating current of the Lambda(b), the semileptonic Lambda(b) --> Lambda l(+)l(-) transition is investigated in the framework of the light cone QCD sum rules. Sum rules for all 12 form factors responsible for the Lambda(b) --> Lambda l(+)l(-) decay are constructed. The obtained results for the form factors are used to compute the branching fraction. A comparison of the obtained results with the existing predictions of the heavy quark effective theory is presented. The results of the branching ratio shows the detectability of this channel at the Large Hadron Collider beauty in the near future is quite high.