Pesachim, Chapter 4, Mishnah 4. This Mishnah lists several types of local custom, practices that some places observed and others did not. The first of them concerns the Pesach offering.
Eating Roasted Meat on the Nights of Pesach:
"Makom shenahagu le'echol tzli b'leilei Pesachim - ochlin; makom shenahagu shelo le'echol - ein ochlin" - in a place where the custom is to eat roasted meat on the nights of Pesach, it is permitted to eat it; and in a place where the custom is not to eat it, it should not be eaten.
What is the reason behind the custom not to eat roasted meat? Since we do not have the Beis Hamikdash, the practice looks as though a person is eating from the meat of the Pesach offering outside Jerusalem and outside the Beis Hamikdash, which is of course forbidden. In order to avoid this appearance, some places adopted the custom not to eat roasted meat on the night of Pesach, while other places did eat it.
Lighting a Lamp on the Night of Yom Kippur:
The Mishnah continues with another custom, this one concerning Yom Kippur: "Makom shenahagu l'hadlik es hanair b'leilei Yom Hakippurim - madlikin; makom shenahagu shelo l'hadlik - ein madlikin".
The Gemara explains that both customs, both those who light a lamp and those who do not, are aimed at one and the same result. Marital relations are forbidden on the night of Yom Kippur, and in order to ensure that a person does not come to that, the customs diverged:
Those who light: since a person does not have relations with his wife in a lit room, the light itself prevents them from doing so.
Those who do not light: on the contrary, the light draws husband and wife to one another, whereas in the dark they will not be drawn to each other, and therefore a lamp should not be lit.
Although both customs are aimed at a single goal, the Mishnah concludes and rules: "Umadlikin b'vatei kenesios uv'vatei midrashos uvimvo'os ha'afeilim v'al gabei hacholim" - in shuls and study halls, in dark alleyways and for the needs of the sick. In any such place, where a husband and wife do not sleep, the concern is not relevant at all, and there is no custom either to light or not to light. According to both customs alike it is permitted to light a lamp there, since no couple is sleeping there.
In summary: in this Mishnah we learned two local customs: eating roasted meat on the nights of Pesach, where places differed because of the appearance of eating the Pesach offering outside its proper place; and lighting a lamp on the night of Yom Kippur, where both customs are aimed at one purpose, to prevent a transgression. And we learned that in places where there is no such concern, such as shuls, study halls, dark alleyways and where the sick are found, a lamp is lit according to all opinions.