The approximate computing paradigm advocates for relaxing accuracy goals in applications to improve energy-efficiency and performance. Recently, this paradigm has been explored to improve the energy efficiency of silicon photonic networks-on-chip (PNoCs). In this paper, we propose a novel framework (LORAX) to enable more aggressive approximation during communication over silicon photonic links in PNoCs. This is the first work that considers loss-aware laser power management and multilevel signaling to enable effective data approximation and energy-efficiency in PNoCs. Simulation results show that our framework can achieve up to 31.4% lower laser power consumption and up to 12.2% better energy efficiency than the best known prior work on approximate communication in PNoCs, for the same application output quality.