Source: Tafsir al-Ahlam al-Kabir (Ibn Sirin)
The lamp in a dream is the caretaker of the house, the scholar of the town, or a righteous son. Its light indicates righteousness in religion and worldly life. Its extinguishing indicates the death of whomever it represents or the loss of a blessing.
Source: Ta'tir al-Anam fi Ta'bir al-Manam (Al-Nabulsi)
The lamp indicates a righteous son, a righteous wife, or a good life. A strong lamp light indicates abundant sustenance and relief.
Source: Al-Isharat fi Ilm al-Ibarat (Ibn Shahin)
The lamp is interpreted as knowledge, guidance, and faith. Whoever sees himself lighting a lamp will be blessed with a knowledgeable son or will repent from his sins.