The LENA device has undergone all of the required testing for electronic devices, which you can read about here.

Unlike a cell phone or Bluetooth device, the LENA device is a recording device only. It is not designed to transmit signals, meaning that it does not produce large amounts of radio frequency emissions. By virtue of having electronic components, it emits a small amount of electromagnetic interference, as do battery-operated toys, hearing aids, and the like. The interference is not enough to be dangerous.