Redox active electrode materials derived from organic precursors are of interest for use as alternative cathodes in Li batteries due to the potential for their sustainable production from renewable resources. Here, a series of organic networks that either contain triazine units or are derived from triazine-containing precursors are evaluated as cathodes versus Li metal anodes as possible active materials in Li batteries. The role of the molecular structure on the electrochemical performance is studied by comparing several materials prepared across a range of conditions allowing control over functionality and long-range order. Well-defined structures in which the triazine unit persists in the final material exhibit very low capacities at voltages relevant for cathode materials (<10 mA·h g–1). Relatively high, reversible capacity (around 150 mA·h g–1) is in fact displayed by amorphous materials with little evidence of triazine functionality. This result directly contradicts previous suggestions that the triazine unit is responsible for charge storage in this family of materials. While the gently sloping discharge and charge profiles suggest a capacitive-type mechanism—further confirmed by the trend of increasing capacity with increasing surface area—electron paramagnetic resonance (EPR) spectroscopy studies show that the materials exhibiting higher capacities also display substantial EPR signals, potentially implicating unpaired spins in a charge storage mechanism that could involve charge transfer.