Q. Can someone that started Shabbos early ask his neighbor that davens late to turn on the lights for him?
A. Shulchan Aruch (O. H. 263: 17) rules that it is permitted for someone that has already accepted Shabbos to ask another that has not, to do a melocho for him. Mishna Berura (ibid.64) warns that this should not be done when it is already too close to sunset, as the majority of the community has already received Shabbos and the few that have not would be drawn by them.
(In relation to the previous questions, this does not apply to telling an Israeli resident who temporarily travels to Chutz Laaretz, to do melochos for him on the second day of Yom Tov, see Minchas Itzchok 7, 34).
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit"a