Well for one thing, the winged dice represent the wings of "chance". The lamp, the genie, the rainbow, the stars represents the good things in life... the lamp and genie (wishes). The rainbow could mean wealth (with the pot of gold in the end) and life (as in a colorful life). The stars could mean fame or success. Why did I say the person is very lucky? Because the dice came from the hands of the genie so it is SURE to be a winning dice - a very lucky dice - a very lucky chance! Hence, the owner of the lamp is a very lucky person.
hahaha. Does this make any sense? Sorry for this long interpretation.