We consider scheduling distributed real-time tasks in unreliable (e.g., those with arbitrary node and network failures) and untrustworthy systems (e.g., those with Byzantine node behaviors). We present a distributed real-time scheduling algorithm called LRTG. The algorithm makes two novel contributions. First, LRTG uses gossip for reliably propagating task scheduling parameters and for discovering task execution nodes. Second, the algorithm guards against potential disruption of message propagation due to Byzantine attacks using a mechanism called LASIRC. By doing so, the algorithm provides assurances on task timeliness behaviors, despite system unreliability and untrustworthiness. Our performance evaluation shows LRTG's effectiveness.