According to the Sixth Doctor televised adventure, "Attack of the Cybermen", the answer is somewhat ambiguous. It certainly could be said that he died fighting the Cyber-Controller. However, there's a case to be made for saying the Doctor indirectly killed him by freeing him from the machines that were converting him into a Cyberman. Had he not been freed, he would likely have "lived" as a fully converted Cyberman. It's also possible that the Doctor might have been able to have more successfully disconnected Lytton from the Cyber-conversion machines had he not been working so hastily.