Q. Is it better if one lights the yortzait candle usually used on the second day Yom Tov when they say Izkor, before Shabbos (you would need a 72 hour candle) since it is not really needed for Yom Tov?

A. Shulchan Aruch (O.H. 514: 5) rules that one should not light an unnecessary candle on Yom Tov, unless it is required for a specific Yom Tov need. Candles for shul illumination are permitted since they provide honour to the consecrated site, and they are permitted even if no one is present. (Mishna Berura ibid. 34.) Candles for a mitzva like a bris mila are also allowed (ibid. 30.)
However, in regards to Yortzait or Izkor candles Poskim maintain that it is better to light them before Yom Tov (Ksav Sofer quoted by Biur Halocho ibid. d’h Ner) or by the Yom Tov table to add light to the room or in Shul as above. (ibid.)
Nitei Gavriel (Yom Tov 1: 55: 2 – n. 4) writes that his own minhag is to light a candle for Dovid Hamelech’s yortzait at the end of the first day of Shavuos in shul and to learn immediately Torah by it’s light.
When in need, one can light them anywhere, since after all they are lit for the mitzva of honouring one’s parents. (Biur Halocho and Ksav Sofer ibid.)
Horav Shlomo Miller’s Shlit”a minhag is to light before the beginning of Yom Tov or the preceding Shabbos.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a