May one light Shabbos candles if he/she did not perform Eruv Tavshilin?
If one did not perform Eruv Tavshilin, and is not giving his candles to another person to light for him [see next], then he may light one Shabbos candle by the table which the meal will be eaten on. One may not light more than one Shabbos candle, [and may not light the candle in an area that one is not eating]. [See footnote regarding the law today being that all homes have electric light.]
Giving the candles to another person to light for him: If there is another person available that performed Eruv Tavshilin, then one may give him all the Shabbos candles as a legal present, and have him then light all the Shabbos candles on ones behalf. The candles are permitted to be lit by that person even in the house of the giver [i.e. the person who did not perform Eruv Tavshilin]. It is forbidden for that person to light the candles until they are given to him as a present. [When giving the candles to another person there is no limit in the amount of candles that may be given and subsequently lit on ones behalf. In the event that one gives his candles to another person to light for him it is forbidden for him to light even one candle himself, as the lighting of one candle was only permitted when one is not having another person light any candles on one’s behalf.]
The Michaber 527/19 records a dispute in Poskim regarding whether one may light Shabbos candles on Erev Shabbos which is Yom Tov if he did not perform Eruv Tavshilin. Some Poskim [Rambam; Rif] rule that one is not required to say the Nussach of “to light” when performing the Eruv, hence proving that one may light Shabbos candles even if he did not place an Eruv on Erev Yom Tov. [Beis Yosef 527; first opinion in Michaber ibid; Shulchan Gavoa 527/27; Nehar Shalom 527/10; Mamar Mordechai 527/18] According to this opinion one may light as many candles as he desires. [Elya Raba 527/24; Nehar Shalom ibid; Kaf Hachaim 527/111] Other Poskim [Rosh; Tur; Ran] however rule one is required to say “to light” within the Nussach of the Eruv, hence proving that if one did not perform an Eruv then he may not light candles. [second opinion in Michaber ibid] Practically some Poskim rule that one may be lenient to light Shabbos candles as rules the first opinion. [Bach 527; Kneses Hagedola 527/16 that so is the custom; Elya Raba 527/25; Birkeiy Yosef 527/9] Nevertheless one should not light more than one candle. [M”A 527/18; Nehar Shalom ibid; M”B 527/55 and Shaar Hatziyon 80; Kaf Hachaim 527/112 in his opinion of Michaber ibid] The ruling of Admur in this matter is as follows: Admur omits the dispute above brought in Michaber and simply writes [529/28] that if one did not do Eruv Tavshilin then it is forbidden for him to light any candles. Thus we see Admur rules like the stringent opinion of the Michaber ibid. Nevertheless Admur concludes that this law follows the same law as cooking food for Shabbos in which the Michaber 527/20 rules that one is to acquire his food to a neighbor who did an Eruv and have him cook his food for him, and if a neighbor is not available then one may cook one dish for Shabbos. On this basis Admur likewise rules [527/29] that one can acquire the food and candles to a neighbor for him to cook and light on his behalf, or if a neighbor is not available or one does not desire to acquire his food and candles to the neighbor, then one may cook one dish and light one candle. Hence we see Admur takes an interesting approach in his final ruling of the subject and rules that one may always light one candle if he did not acquire it to others just like one may cook one dish, [irrelevant of the dispute ibid]. Nevertheless if one does acquire candles to others then one may not light any candles, as rules the stringent opinion in Michaber ibid.
 This applies whether there is no person available to acquire the candles to, or even if there is a person available but one does not desire to do so for whatever reason, nevertheless one may light one candle in the area of eating. [Admur ibid; Rashal; M”A 527/20; Elya Raba 527/27; Chayeh Adam 102/14; M”B 527/61; Kaf Hachaim 527/29] Vetzaruch Iyun if one can acquire food to a neighbor to be cooked on one’s behalf and not give him the candles, or if when one desires to give the neighbor his food then he must also give him his candles to light for him. From M”B 527/61 it is evident that one is not required to give him both the food and candles.
Other opinions: Some Poskim rule that if one is able to acquire the food [and candles] to a neighbor and have him cook [and light] for him, then it is forbidden for him to cook or light any candles, and he rather must have the other person do so for him, as explained next. [Darkei Moshe 527/7]
 Admur ibid; M”A 527/18; M”B 527/55; Kaf Hachaim 527/112
The reason: If one will not be acquiring his food and candles to another person to cook and light for him, then due to the honor of Shabbos the Sages allowed him to prepare all the Shabbos necessities in small amount to simply be able to live the day. Thus one may bake one loaf of bread and cook one pot of food, and may light one candle neat the area that he will eat. The reason this candle may be lit is because of Shalom Bayis, in order so a person will not eat in the dark. Furthermore, even without eating one does not have Shalom Bayis without light in his home. [Admur ibid]
Other opinions: Some Poskim rule one may light as many candles as one desires. [See Poskim brought in Background]
 So is implied from Admur ibid which states “One candle which one will eat by. However in a room that one will not be eating it is forbidden to light a candle there for the sake of Shabbos”. However in the conclusion of the Halacha Admur states “even without eating one does not have Shalom Bayis without light in his home”, hence implying that one may light one candle even if he will not be eating at all at home. Vetzaruch Iyun!
 Perhaps today being that we all have electricity and one will hence not eat in the dark even if he does not light one candle, then even one candle should not be lit, as the reason for the allowance of the Sages is no longer relevant. We find a similar ruling in M”B 527/62 and Kaf Hachaim 527/121 that if one already has one loaf then he may not bake another one, and the same should apply regarding lighting candles today when we have electricity. Vetzaruch Iyun
 So is clearly evident from Admur 527/29 that permits lighting one candle only if one did not acquire the candles to others to light for him. See Background ibid for other opinions on this matter.