Lapis is a rock and not a mineral because it is made up from various other minerals. To be a true mineral it would have one constituent only.
The first part of the name is the Latin lapis, meaning stone. The second part, lazuli, is the genitive form of the medieval Latin lazulum, a loanword adapted from the Arabic (al-)lazward, itself a borrowed word from the Persian لاژورد lazhward. This was originally a place-name, but soon came to mean blue because of its association with the stone. English azure, Spanish azul, Italian azur also derives from this source. Taken as a whole, lapis lazuli means stone of azure.
Description
The main component of lapis lazuli is lazurite (25 to 40 percent), a feldspathoid silicate mineral composed of sodium, aluminium, silicon, oxygen, sulfur, and chlorine. Most lapis also contains calcite (white), sodalite (blue) and pyrite (yellow). Other possible constituents are augite, diopside, enstatite, mica, hauynite, hornblende and nosean. Lazurite's formula is (Na,Ca)8(AlSiO4)6(S,SO4,Cl)1-2 [1].
Lapis lazuli usually occurs in crystalline limestones as a result of contact metamorphism.

A Mesopotamian lapis lazuli pendant circa 2900 BC.

A carving in high quality lapis lazuli, showing gold-colored inclusions of pyrite. These inclusions are common in lapis and are an important help in identifying the stone. The carving is 8 cm (3 inches) long
The finest color is intense blue, lightly dusted with small flecks of golden pyrite. There should be no white calcite veins and the pyrite inclusions should be small. Stones that contain too much calcite or pyrite are not as valuable. Patches of pyrite are an important help in identifying the stone as genuine and do not detract from its value. Often, inferior lapis is dyed to improve its color, but these are often a very dark blue with a noticeable grey cast.
Sources
The finest lapis comes from the Badakshan area of Afghanistan. This source of lapis may be the oldest continually worked set of mines in the world, the same mines operating today having supplied the lapis of the pharaohs. More recently, during the Soviet war in Afghanistan, Afghani resistance fighters disassembled unexploded Russian landmines and ordnance and used the scavenged explosive to help mine lapis to further fund their resistance efforts.
In addition to the Afghan deposits, lapis has been found in the Andes near Ovalle, Chile, where it is usually pale rather than deep blue. Other less important sources are the Lake Baikal region of Russia, Siberia, Angola, Burma, Pakistan, USA (California and Colorado) and Canada.
Uses
Lapis takes an excellent polish and has been made into jewelry, carvings, boxes, mosaics, ornaments and vases. In architecture it has been used for cladding the walls and columns of palaces and churches.
It was also ground and processed to make the pigment Ultramarine for tempera paint and, more rarely, oil paint. Its usage as a pigment in oil paint ended in the early 19th century as a chemically identical synthetic variety, often called French Ultramarine, became available.
Enhancements
The most common enhancement for lapis lazuli is dyeing (staining), where a stone with white calcite inclusions is stained blue to improve the colour. Other enhancements commonly seen are waxing and resin impregnations, again to improve colour. The colour of stained lapis is unstable and will fade with time.
Cultural and historical/mythical usage
In ancient times, lapis lazuli was known as sapphire, which is the name that is used today for the blue corundum variety sapphire. It appears to have been the sapphire of ancient writers because Pliny refers to sapphirus as a stone sprinkled with specks of gold. A similar reference can be found in the Hebrew Bible in Job 28:6.
In ancient Egypt lapis lazuli was a favorite stone for amulets and ornaments such as scarabs; it was also used by the Assyrians and Babylonians for seals. Egyptian burial sites dating before 3000 B.C. contained thousands of jewelry items, many of lapis. Powdered lapis was used by Egyptian ladies as a cosmetic eye shadow.
As inscribed in the 140th chapter of the Egyptian Book of the Dead, lapis lazuli, in the shape of an eye set in gold, was considered an amulet of great power. On the last day of the month, an offering was made before this symbolic eye, for it was believed that, on that day, the supreme being placed such an image on his head.
The ancient royal Sumerian tombs of Ur, located near the Euphrates River in lower Iraq, contained more than 6000 beautifully executed lapis lazuli statuettes of birds, deer, and rodents as well as dishes, beads, and cylinder seals. These carved artifacts undoubtedly came from material mined in Badakhshan in northern Afghanistan. The word lazuli itself originates from the Persian dialect of Badakhshan.
The Romans believed that lapis was a powerful aphrodisiac. In the Middle Ages, it was thought to keep the limbs healthy, and free the soul from error, envy and fear.
It was once believed that lapis had medicinal properties. It was ground down, mixed with milk and applied as a dressing for boils and ulcers.
Many of the blues in painting from medieval Illuminated manuscripts to Renaissance panels were derived from lapis lazuli. Ground to a powder and processed to remove impurities and isolate the component lazurite, it forms the pigment ultramarine. This clear, bright blue, which was one of the few available to painters before the 19th century, cost a princely sum. As tempera painting was superseded by the advent of oil paint in the Renaissance, painters found that the brilliance of ultramarine was greatly diminished when it was ground in oil and this, along with its cost, led to a steady decline in usage. Since the synthetic version of ultramarine was discovered in the 19th century (along with other 19th century blues, such as cobalt blue), production and use of the natural variety has almost ceased, though several pigment companies still produce it and some painters are still attracted to its brilliance and its romantic history.