The measurements of particle multiplicity distributions have generated considerable interest in understanding the fluctuations of conserved quantum numbers in the Quantum Chromodynamics (QCD) hadronization regime, in particular near a possible critical point and near the chemical freeze-out. We report the measurement of efficiency and centrality bin width corrected cumulant ratios ($C_{2}/C_{1}$, $C_{3}/C_{2}$) of net-$Lambda$ distributions, in the context of both strangeness and baryon number conservation, as a function of collision energy, centrality and rapidity. The results are for Au + Au collisions at five beam energies ($sqrt{s_{NN}}$ = 19.6, 27, 39, 62.4 and 200 GeV) recorded with the Solenoidal Tracker at RHIC (STAR). We compare our results to the Poisson and negative binomial (NBD) expectations, as well as to Ultra-relativistic Quantum Molecular Dynamics (UrQMD) and Hadron Resonance Gas (HRG) model predictions. Both NBD and Poisson baselines agree with data within the statistical and systematic uncertainties. The ratios of the measured cumulants show no features of critical fluctuations. The chemical freeze-out temperatures extracted from a recent HRG calculation, which was successfully used to describe the net-proton, net-kaon and net-charge data, indicate $Lambda$ freeze-out conditions similar to those of kaons. However, large deviations are found when comparing to temperatures obtained from net-proton fluctuations. The net-$Lambda$ cumulants show a weak, but finite, dependence on the rapidity coverage in the acceptance of the detector, which can be attributed to quantum number conservation.
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