Vibration energy harvesting based on piezoelectric transducers is an attractive choice to replace single-use batteries in powering Wireless Sensor Nodes (WSNs). As of today, their widespread application is hindered due to low operational bandwidth and the conventional use of lead-based materials. The Restriction of Hazardous Substances legislation (RoHS) implemented in the European Union restricts the use of lead-based piezoelectric materials in future electronic devices. This paper investigates lithium niobate ($LiNb{O}_3$) as a lead-free material for a high-performance broadband Piezoelectric Energy Harvester (PEH). A single-clamped, cantilever beam-based piezoelectric microgenerator with a mechanical footprint of 1 cm², working at a low resonant frequency of 200 Hz, with a high piezoelectric coupling coefficient and broad bandwidth, was designed and microfabricated, and its performance was evaluated. The PEH device, with an acceleration of 1 g delivers a maximum output RMS power of nearly 35 μW/cm² and a peak voltage of 6 V for an optimal load resistance at resonance. Thanks to a high squared piezoelectric electro-mechanical coupling coefficient ($k^2$), the device offers a broadband operating frequency range above 10% of the central frequency. The Mason electro-mechanical equivalent circuit was derived, and a SPICE model of the device was compared with experimental results. Finally, the output voltage of the harvester was rectified to provide a DC output stored on a capacitor, and it was regulated and used to power an IoT node at an acceleration of as low as 0.5 g.