Why a lamp?
The Mishnah in "Bameh Madlikin" (Shabbat ch. 2) deals with fit oils and wicks. The Gemara (Shabbat כ״ג ע״ב (23b)) rules: the household lamp takes precedence over the Chanukah lamp, because of domestic peace.
Proof for the "domestic peace" basis: when one cannot afford both, the Shabbat lamp comes first - even before daytime wine.