Stimulated emission (SE) was measured from two InGaN multiple quantum well (MQW) laser structures with different QW In compositions x. SE threshold energy densities (Ith) increased with increasing x-dependent QW depth. Time-resolved differential transmission measurements mapped the carrier relaxation mechanisms and explained the dependence of Ith on x. Carriers are captured from the barriers to the QWs in <1 ps, while carrier recombination rates increased with increasing x. For excitation above Ith, an additional, fast relaxation mechanism appears due to the loss of carriers in the barriers through a cascaded refilling of the QW state undergoing SE. The increased material inhomogeneity with increasing x provides additional relaxation channels outside the cascaded refilling process, removing carriers from the SE process and increasing Ith.