Wireless sensor nodes (WSNs) are the fundamental part of an Internet of Things (IoT) system for detecting and transmitting data to a master node for processing. Several research studies reveal that one of the disadvantages of conventional, battery-powered WSNs, however, is that they typically require periodic maintenance. This paper aims to contribute to existing research studies on this issue by exploring a new energy-autonomous and battery-free WSN concept for monitor vibrations. The node is self-powered from the conversion of ambient mechanical vibration energy into electrical energy through a piezoelectric transducer implemented with lead-free lithium niobate piezoelectric material to also explore solutions that go towards a greener and more sustainable IoT. Instead of implementing any particular sensors, the vibration measurement system exploits the proportionality between the mechanical power generated by a piezoelectric transducer and the time taken to store it as electrical energy in a capacitor. This helps reduce the component count with respect to conventional WSNs, as well as energy consumption and production costs, while optimizing the overall node size and weight. The readout is therefore a function of the time it takes for the energy storage capacitor to charge between two constant voltage levels. The result of this work is a system that includes a specially designed lead-free piezoelectric vibrational transducer and a battery-less sensor platform with Bluetooth low energy (BLE) connectivity. The system can harvest energy in the acceleration range [0.5 g-1.2 g] and measure vibrations with a limit of detection (LoD) of 0.6 g.