Life, the LIGHT of divinity, wisdom, intellect, and good works are all manifestations of the symbolic nature of lamps. Lamps are also a gateway to another planes of dimensions, brings protection against dark demons, and can be the illumination of the spirit. Lamps are said to be a pinnacle symbol of self-sacrifice, as it consumes itself to offer light to the world.
Solomon was the only person with the power to control genies. To any other human a genie was an unstoppable being of fire, smoke, and wind. A genie in a lamp, then, is significant because it shows that no matter how powerful something or someone is, it can always be controlled.
Like angels, genies represent beings which exist beyond our realm of perception. Genie lamps correspond to connections between the normal world and a greater universe of which we might not be aware.