I remember few years back I checked it. Piezo element I took it from a beeping buzzer like bike indicator one. I connected piezo to DSO without any load. Then I tapped it from one side, I noted the reading at +ve side 32 to 38 volt and negative side some 6 to 8 volt. Then I continued the test with different loads like resistor, capacitor and different values I noticed for a small load also voltage reduces drastically. Voltage came down to 5 to 7 volt at +ve side around 1 volt at -ve side. This happens because it generates enough voltage but current is very less.
When u connect a LED at this environment one possibility LED will get damage in a short period. So u need a Zener to protect it and if u connect a small value capacitor it can store small amount of current which will extent LED glow time. Preferably use a diode in series with piezo at right direction to avoid -ve voltage. If u want more power u need more piezo elements.