Relativistic, charged particles present in extensive air showers lead to a coherent emission of radio pulses which are measured to identify the shower initiating high-energy cosmic rays. Especially during thunderstorms, there are additional strong electric fields in the atmosphere, which can lead to further multiplication and acceleration of the charged particles and thus have influence on the form and strength of the radio emission. For a reliable energy reconstruction of the primary cosmic ray by means of the measured radio signal it is very important to understand how electric fields affect the radio emission. In addition, lightning strikes are a prominent source of broadband radio emissions that are visible over very long distances. This, on the one hand, causes difficulties in the detection of the much lower signal of the air shower. On the other hand the recorded signals can be used to study features of the lightning development. The detection of cosmic rays via the radio emission and the influence of strong electric fields on this detection technique is investigated with the LOPES experiment in Karlsruhe, Germany. The important question if a lightning is initiated by the high electron density given at the maximum of a high-energy cosmic-ray air shower is also investigated, but could not be answered by LOPES. But, these investigations exhibit the capabilities of EAS radio antenna arrays for lightning studies. We report about the studies of LOPES measured radio signals of air showers taken during thunderstorms and give a short outlook to new measurements dedicated to search for correlations of lightning and cosmic rays.