Significance of Lighting Ghee/Oil Lamp before Deity.
God is Akanda Jyothi Swaropa LIGHT is the first and foremost manifestation of God
Hindus Light oil Lamps daily in Pooja Mandir in the morning and evening, because it, the JYOTI itself is Bhagawaan We invite HIM with these Symbolic lamps.
Oil lamps have represented spirit and spiritual ideas since ancient times.
The oil or ghee in the lamp symbolizes our vaasanas or negative tendencies and the wick, the ego. When lit by spiritual knowledge, the vaasanas get slowly exhausted and the ego too finally perishes. The flame of a lamp always burns upwards. Similarly we should acquire such knowledge as to take us towards higher ideals.

There is another meaning to lighting a lamp with Ghee, oil or burning a candle
If a lamp is lit with pure ghee made from cows milk, the vibrations are said to be in communion with Gods & deities

If a lamp is lit with oil (Please note here that different oils have different effects), the vibrations are said to be in communion with our ancestors

If a candle (meaning wax made) is lit, the vibrations are said to be in communion with demons and evil spirits.
("Secret Forces Behind Life" by Swami Dattavadhut)
Burning of animal carbon in the form of ghee in lamps in small doses is conducive for removing toxins in the body and the use of mahua or iluppai oil is considered very good for eyes. Electric lights do not have this use.

Traditionally the lighting of the lamp is also a part of Bhutaaradhana (element worship).
Lighting a lamp for Agni
Placing water for Jala
Incense stick smoke for Vayu
Sandal paste, Bhasma, vermilion for Prithvi
Deep meditative prayer for Akas

Cotton Wicks and their significance:

Single wick (Eka Mukha Deepam) for normal benefit.
Two wicks (Dwimukha deepam) bring harmony and peace in the family and relatives.
Three wicks (Trimukha Deepam) Blesses with progeny.
Four wicks (Chathurmukha deepam) bring all-round prosperity and sumptuous food.
Five wicks (Panchamkukha deepam) showers akhanda aishwaryam or Wealth.
Six wicks (Shanmukha deepam) blesses with Akhanda Gyana (Knowledge) & Vairagyam (Renunciation).

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Directions for lighting lamps and their importance:

North - For success in all ventures undertaken. Most preferable direction to place and light a lamp:
East For good health and peace of mind.
West For freedom from debts and victory over enemies