Despite its remarkable success, the standard LCDM paradigm has been challenged lately by potential tensions in the Hubble Constant measurements, as well as a slight mismatch between simulations and observations on smaller scales. This has reinvigorated interest in beyond-LCDM models, such as Dark Matter interacting either with standard model particles or with an additional dark sector. These interactions result in a suppression of the matter power spectrum on small scales, making them an ideal target to be constrained with Lyman-alpha data. In this talk I will present a novel parameterisation of this small-scale power suppression, which allows these models to be constrained with Lyman-alpha data without needing new computationally expensive hydrodynamical simulations for each set of model parameters.