Lapis Lazuli is a rock not a mineral. It is primarily composed of lazurite, calcite and pyrite. However the exact composition of the rock varies from location to location. It is usually found within limestones which have been heavily altered during high grade metamorphism.
Lapis has been mined in Afghanistan for about 9000 years and this has been the key source of Lapis for most of history. Secondary deposits have since been found in other locations, most famously Chile. Since there is chemical variation from location to location, it is possible to pinpoint the locality of a sample of Lapis. This technique is sometimes used when looking at antique art which has been painted with the pigment ultramarine.
The blue colour is not due to the presence of copper, but to the behaviour of the sulphur ions within huayne. Unlike many brightly hued compounds, Lazulite is chemically very stable and pigments which use Lapis as a basis stay true to colour over thousands of years.