In this paper, we explore perpetual, scalable, Low-powered Wide-area networks (LPWA). Specifically we focus on the uplink transmissions of non-orthogonal multiple access (NOMA)-based LPWA networks consisting of multiple self-powered nodes and a NOMA-based single gateway. The self-powered LPWA nodes use the "harvest-then-transmit" protocol where they harvest energy from ambient sources (solar and radio frequency signals), then transmit their signals. The main features of the studied LPWA network are different transmission times-on-air, multiple uplink transmission attempts, and duty cycle restrictions. The aim of this work is to maximize the time-averaged sum of the uplink transmission rates by optimizing the transmission time-on-air allocation, the energy harvesting time allocation and the power allocation; subject to a maximum transmit power and to the availability of the harvested energy. We propose a low complex solution which decouples the optimization problem into three sub-problems: we assign the LPWA node transmission times (using either the fair or unfair approaches), we optimize the energy harvesting (EH) times using a one-dimensional search method, and optimize the transmit powers using a concave-convex (CCCP) procedure. In the simulation results, we focus on Long Range (LoRa) networks as a practical example LPWA network. We validate our proposed solution and we observe a $15\%$ performance improvement when using NOMA.