In Hilchos Channukah (OC Siman 675 Sif 1 -- See also there Mishneh Brurah Sif-Katan 3.) We learn that if one lit Channukah candles (for the mitzvah) from the day before and they stayed lit until the following day still he must extinguish the candle(s) and re-light it now for the sake of the mitzvah (of ner channukah) since each day is a mitzvah in and of itself.
What about in regards to Shabbos. If someone lit Shabbos candles Erev Shabbos Parshas Chayeh Sarah (for example) and they stayed lit until Erev Shabbos Parshas Toldos and would easily burn well into the night, is this enough? Or must new candles be lit in honor of this Shabbos? The main reasons for Shabbos candles is for Shalom Bayis in order one may see around the house. As well the enjoyment one has by eating by the candles. Seemingly these 2 things are fulfilled with the candles that remained lit from the previous Shabbos.
Yehoshua, Yerushalayim, Eretz Yisrael
While it is true that Ner Shabbos was instituted by Chazal for Shalom Bayis and for Oneg Shabbos, nonetheless it is clear that there is a new Mitzvah each Friday to light Ner Shabbos and that if someone does not light on a particular Erev Shabbos because his candles are still burning from last week, he has neglected a positive Mitzvah.
I quote the Biur Halachah (263:4, D"H m'b'Od Yom): "If he lit before Plag haMinchah for the sake of Shabbos, even if he accepted upon himself Shabbos from that time, his lighting does not help at all, even b'di'Avad, and he needs to extinguish [the candles] and re-light and make another Berachah". This is speaking about someone who lit a few hours before Shabbos, all the more so someone that lit last week. So we see that one has to do the Mitzvah each week and that it needs to be done within Plag haMinchah.
Also, remember Rashi in Parshas Chayei Sarah (24:67) who quotes the Midrash that says that when Sarah was alive there was a candle lit in her tent from Erev Shabbos to Erev Shabbos. If this candle was anyway burning miraculously why did it stop on Erev Shabbos (either because she put it out or it went out by itself)? Why not burn forever? The answer seems to be that Sarah had a Mitzvah each Erev Shabbos to light the candle anew.
This is not a Psak Halachah
I dont think your example from the Biur Halacha is good becuase there he lit them originally at the "wrong"time. The questioner asked what if he lit them b'heter at the correct time on shabbos #1
While it is true that Shalom Bayis and Oneg Shabbos depend on the candles being lit and not on the act of lighting, it is clear that the act of lighting the candles was instituted as the Mitzvah, as we see from the Nusach of the Berochah - l'Hadlkik Ner Shel Shabbos. Would anyone suggest that, in the situation described by the one asking the question, that one could make the Berochah on Shabbos #2? I think that it is self evident that he cannot. Someone who did not light Shabbos candles, but only arranged that lights would be on in the house for Shabbos, has certainly enhanced Shalom Bayis and Oneg Shabbos, but he has not performed the Ma'aseh Mitzvah of Ner Shabbos and he cannot make the Berochah. So if we accept this premise that it is the act of lighting that is the Mitzvah, then it is reasonable to assume that every Shabbos has its own obligation to light, in the same way that every Rosh haShanah has its own obligation to blow Shofar and every Pesach has its own obligation to eat Matzah. Therefore, lighting the candles the previous Shabbos is no different then lighting the candles too early in the afternoon, and he would have to extinguish them and light them again as implied in the Biur Halachah and the Midrash.
ok I understand your distinction.
but to change the subject just a little you wrote: "Someone who did not light Shabbos candles, but only arranged that lights would be on in the house for Shabbos, has certainly enhanced Shalom Bayis and Oneg Shabbos, but he has not performed the Ma'aseh Mitzvah of Ner Shabbos and he cannot make the Berochah"
Someone asked me last week that his wife was told by a friend (they follow sfardi minhogim) that you need to turn the electric lights out before you light Shabbos candles, I had never heard this.
The next day he brought in a sefer which quote R' Ovadia Yosef that one does not have to turn off electric lights