  We study consequences of the non-forward amplitude for the semileptonic
baryon decay Lambda_b into Lambda_c which will be measured in detail at LHCb.
We obtain a sum rule for the subleading elastic Isgur-Wise (IW) function A(w)
that originates from the kinetic part of the O(1/mQ) effective Lagrangian
perturbation. In the sum rule appear only the intermediate states J^P=1/2+, the
same that contribute to the O(1/mQ)^2 correction to the axial-vector form
factor G1(w) involved in the differential decay rate at zero recoil w=1. This
allows us to obtain a lower bound on the correction -delta^(G1)_(1/mQ^2) in
terms of A(w) and the shape of the leading elastic IW function xi(w). Another
theoretical implication is that A'(1) must vanish in the limit where the slope
of the xi(w) saturates its lower bound. A strong correlation between the
leading IW function and the subleading one A(w) is thus established in the case
of the baryons.
