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. Net-protons and net-kaons have been used as proxies for the net-baryon number and net-strangeness, respectively. We report the measurement of efficiency- and centrality-bin width-corrected cumulant ratios (C2/C1, C3/C2) of net-Λ 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 (sNN=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 ultrarelativistic 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. UrQMD describes the measured net-ΛC1 and C3 at 200 GeV reasonably well but deviates from C2, and the deviation increases as a function of collision energy. 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 Λ freeze-out conditions similar to those of kaons. However, large deviations are found when comparing with temperatures obtained from net-proton fluctuations. The net-Λ 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.