LTE-based satellite systems in LEO constellations are a promising solution for extending broadband coverage to areas not connected to a terrestrial infrastructure. However, the large delays and Doppler shifts over the satellite channel pose severe technical challenges to a traditional LTE system. In this paper, two architectures are proposed for a LEO mega-constellation realizing a satellite-enabled LTE system, in which the on-ground LTE entity is either an eNB (Sat-eNB) or a Relay Node (Sat-RN). Focusing on the latter, the impact of large delays and Doppler shifts on LTE PHY/MAC procedures is discussed and assessed. It will be shown that, while carrier spacings, Random Access, and RN attach procedures do not pose specific issues, HARQ requires substantial modifications. Moreover, advanced handover procedures will be also required due to the satellites' movement.