A dilemma was a situation which involved two or more difficult choices. A dilemma which involved choices that conflicted with one's ethics or morals was an ethical dilemma.
In 2368, Captain Jean-Luc Picard was faced with the dilemma of the planet Penthara IV slowly turning to ice which would result in thousands, maybe tens of thousands of deaths, in a matter of weeks. Lieutenant Commander Geordi La Forge's solution had extremely critical margins of error, but there would be no more threat if successful. If not successful, then every living thing on the planet would perish, resulting in millions of deaths instead. While Picard wanted the help of time traveler Berlinghoff Rasmussen, who claimed to have come from the 26th century, Picard did not want to know the outcome of his efforts, and because of everything that Starfleet stood for and everything that Picard believed in, he could not ask Rasmussen for that. Picard however noted that there were twenty million lives on the planet and Rasmussen knew what happened to them. Rasmussen took this as a sign that Picard had another dilemma; one that questioned his convictions. (TNG: "A Matter Of Time")