Rabbi Meir says, "One may move any [oil] lamp, except one that has been lit on Shabbat." Rabbi Shimon says, "Only one that is burning on Shabbat. Once it goes out, one may move it."
One of my first memories of Shabbat is a vision of the beauty of the Shabbat candles. Accompanying this memory is the first Shabbat restriction that I recall learning: "We don't touch the Shabbat candles or move them." As I noted in an earlier piece, for our Sages, the Shabbat lights are a way of ensuring shalom bayit—household harmony. One cannot eat, rejoice, or spend meaningful time with family in pitch darkness, but a lighted candle (or oil lamp, in an earlier time) is also an object of anxiety for our Sages. The temptation to move the lamp from place to place can be great: I might want light in my bedroom, as well as my kitchen. The problem here is that the light may go out from the jostling it receives as I retreat down the hall, lamp in hand. Recall that extinguishing is a forbidden labor.
Rabbi Shimon's position looks eminently reasonable. Once the light goes out, then, and only then, may one remove the empty lamp. Rabbi Meir agrees with this position, but moves to outlaw another kind of lamp. If one knows that a lamp has been lit on Shabbat, either by a non-Jew or a Shabbat violator, the lamp must remain in its spot until Shabbat concludes. This is unlike the lamp lit at the onset of Shabbat that may be moved once the fuel has burned up, to make room for other items. At first the requirement to leave the Shabbat violator's lamp untouched, even after the fuel is consumed, seems punitive. However, Rabbi Meir's decree has its own logic: the lamp was withdrawn from our Shabbat existence by forbidden labor, so we withdraw from it—drawing our own boundaries in space for the sake of preserving sacred time.