In simon 276 the famous baal ha'itor that says a goy can do even a malachah d'oraisa for a Jew for a mitzvah. the source for that is the gemarah that speaks about the hot water that was spilled before the milah.
but that case is only where it happened like that, that the water spilled out on shobbos. can someone say that he will not heat up water before shobbos because he will do it on shobbos by a goy? so why in shuls can a goy put on the lights shobbos morning after he shut it at night, isn't it like relying on the goy l'chatchilah?
The Ran in Maseches Shabbos (end of Perek 19) quotes the Ba'al ha'Itur, who told a non-Jew to light a lamp for his Seudah. There is a Mitzvas Asei de'Rabanan to light lamps for Shabbos and to have light by which to eat.
The Ba'al ha'Itur's Heter would seem to be in a situation where the lights went out and for the purpose of the Mitzva he permitted instructing a non-Jew to light the lamps. As the REMA and the Mefarshei Shulchan Aruch point out, this Heter has been extended beyond what was intended.
I have attached an earlier response regarding this topic which might be helpful.
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Shabbos 122: Non-Jew working on Shabbos
In summary, when can and when cannot a non-Jew do work for a Jew on Shabbos?
Is there a special "Heter" for a non-Jew to put on lights for the Jew's Shabbos meal?
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The Kollel replies:
(a) There are two issues to consider in any question of a non-Jew doing Melacha for a Jew on Shabbos.
1. It is forbidden to instruct a non-Jew to perform melacha on Shabbos for a Jew. This applies to both Melacha deOraisa and deRabbanan. Even if the instructions were given to the non-Jew before Shabbos it is still forbidden.
2. We are not allowed to derive any benefit from a Melacha done by a non-Jew specifically for a Jew. This is true even if the non-Jew did the melacha without being told.
In certain circumstances there are exceptions where instruction to a non-Jew is allowed. Instructing the non-Jew to do an Issur d'Rabanan in order to enable us to do a Mitzvah or for the needs of a person who is sick, but not dangerously so, is permitted. (Shulchan Aruch 307 #5) In the above mentioned exceptions it is permitted to tell the non-Jew directly to do Melachah.
(b) Under any other circumstances the following rules apply. When it comes to telling a non-Jew to do Melachah on Shabbat there are three methods of communication.
1. Direct instruction (e.g. Put off the light) This is not permitted under normal circumstances.
2. Indirect instruction (e.g. Why didn't you put of the light last week) This is forbidden on Shabbos but is permitted before Shabbos.
3. Hinting (e.g. It's too light to sleep in here) This is permitted even on Shabbos, remembering that it is Assur to derive direct benefit from the work of a non-Jew. "It is too dark to read in here " would be fine as a hint and would not be an infraction of instructing a non-Jew, however it would be forbidden to read by the light that he switches on as this would be benefitting from Melacha done by a non-Jew specifically for a Jew.
(c) In Siman 276 the Shulchan Aruch discusses the laws of telling a non-Jew to light a lamp. in Se'if 2 the Rama refers to a prevalent Minhag to tell non-Jews to light lamps for the Shabbos meal. This opinion relies on the Ba'al haItur who permitted instructing a non-Jew to do an Issur deOraisa for the purpose of a Mitzva. The Rama points out that the majority of Poskim do not accept the opinion of the Ba'al haItur and it is not proper to rely on it.
(d) In Se'if 4 the Shulchan Aruch rules that if there is already a source of light and the non-Jew adds another light then it is permitted to benefit from the combined effect of the lights as long as the original light continues to burn. In this case you are not considered to be benefitting from the Melacha of the non-Jew.
IN CONCLUSION: The Halachos of instructing a non-Jew are many and detailed. There is a fair amount of unawareness of the issurim involved and the specific circumstances when it is permitted. In all cases it is recommended that a competent Halachic authority be consulted.
Ilan Segal