In classical (i.e., IID) random matrix dynamics, a question that arises frequently is whether the Lyapunov spectrum is "simple." There are several criteria that imply the existence of a maximal number of distinct Lyapunov exponents for random matrix products and these have been used in various applications. Recently, there have been papers extending this classical theory to specific classes of non-stationary matrix products. In this talk, we will discuss two recent papers ([arXiv:2312.03181] and [arXiv.2507.04058]) which establish gaps between non-stationary analogs of Lyapunov exponents. Strategies and key ideas will be presented, with a brief discussion about applications to Anderson localization.