Lighting a Teshuvah candle: On the eve of Shabbos Teshuvah, it is customary in the Rebbe’s household to kindle [a twenty-four-hour candle which is known as] a “Teshuvah light.”[1] [The Rebbe once stated that it is the Chabad custom to light three Teshuvah candles on Erev Shabbos Teshuvah.[2] When the second day of Rosh Hashanah falls on Erev Shabbos, these candles should be lit on Wednesday, Erev Rosh Hashanah, using a 72 hour candle. They may not be lit on Erev Shabbos unless one plans to make a use of the candles on Shabbos, such as if he needs their light for that night.[3]]

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[1] Sefer Haminhagim p. 122 [English]; Sefer Hasichos 1944 p. 7-8; Sicha of Vav Tishrei 1982 [unedited], Hisvadyus 5742 1:67; See Otzer Minhagei Chabad p. 166; Maaseh Melech p. 267 [that the Rebbe would light three candles]; Bakodesh Penima p. 20 [that the Rebbe would light did not light any candles]

[2] Sicha of Vav Tishrei 1982 [unedited], Hisvadyus 5742 1:67; Maaseh Melech p. 267 [that the Rebbe would light three candles]; Bakodesh Penima p. 20 [that the Rebbe would light did not light any candles]

The reason: This corresponds to the three forms of Teshuvah described by Admur in Likkutei Torah Parshas Balak in the Mamar “Mah Tovu”. [ibid]

[3] See Admur 514:13-14; Biur Halacha 514:5 “Ner”; Kaf Hachaim 514:79; Piskeiy Teshuvos 514:14 and 17; Nitei Gavriel Yom Tov 55:2; 88:13; Hilchos Uminhagei Chabad p. 9

The reason: As it is forbidden to light a Ner Shel Batala on Yom Tov. [Admur 514:13; Michaber 514:5] Likewise, the Eruv Tavshilin does not permit performing non meal related Melachas.