Understanding gas flows into and out of the most massive dark matter structures in our Universe, galaxy clusters, is fundamental to understanding their evolution. Gas in clusters is well studied in the hot (> 10 6 K) and cold (< 10 4 K) regimes, but the warm gas component (10 4 -10 6 K) is poorly constrained. It is challenging to observe directly, but can be probed through Lyα absorption studies. We produce the first systematic study of the warm gas content of galaxy clusters through synthetic Lyα absorption studies using cosmological simulations of two galaxy clusters produced with Enzo. We explore the spatial and kinematic properties of our cluster absorbers, and show that the majority of the identified absorbers are due to fast moving gas associated with cluster infall from IGM filaments. Towards the center of the clusters, however, the warm IGM filaments are no longer dominant and the absorbers tend to have higher column densities and metallicities, representing stripped galaxy material. We predict that the absorber velocity distribution should generally be bi-modal and discuss the effects of cluster size, mass, and morphology on the properties of the identified absorbers, and the overall cluster warm gas content. We find tentative evidence for a change in the well known increasing N HI with decreasing impact parameter for the most massive dark matter halos. Our results are compared directly to observations of Lyα absorbers in the Virgo cluster, and provide predictions for future Lyα absorption studies.