First you will need to choose a surface that you would like to create the effect of the lapis lazuli stone.  You may choose smaller objects such as boxes or picture frames, or possibly choose to create the effect of inlaid lapis on a piece of furniture.  It is completely up to your own discretion.
Once you have the object you wish to paint, you should either mask off the specific area, or prep the entire surface with a white gesso and allow to dry thoroughly.  When  you are ready to begin painting, you should keep in mind that the lapis lazuli stone has a drifting Milky Way effect with both very dark and bright areas.  What gives the stone its distinction are the flecked and spattered areas with drifting specks of gold pyrite.
 

(Scanned photograph from Sloan & Gwynn, 1990, p. 102.)	1.  Mix  your French ultramarine acrylic or oil  paint with some glaze using very little white mineral spirit to dilute.  Brush on the central areas of the surface.
(Scanned photograph from Sloan & Gwynn, 1990, p. 102.)	2. Paint in the remaining areas with a mixture of French Ultramarine and Burnt umber pigment.
(Scanned photograph from Sloan & Gwynn, 1990, p. 102.)	3. Mutton cloth the surface to eradicate brush marks.  The blue should look celestial,  clear, and translucent.  Soften with a badger hair brush.
(Scanned photograph from Sloan & Gwynn, 1990, p. 103.)	4. Mix three tones of blue pigment, using French Ultramarine, Titanium White, and Burnt Umber.  Finely spatter the surface in drifts, like the Milky Way.
(Scanned photograph from Sloan & Gwynn, 1990, p. 103.)	5.  Spatter the lightest tone of pigment by pulling back the bristles of the brush with your index finger.
(Scanned photograph from Sloan & Gwynn, 1990, p. 103.)	6.  Very gently, flick a little gold powder in drifts to simulate the flecks of the iron pyrite inclusions.

(Scanned photograph from Sloan & Gwynn, 1990, p. 103.)  7.  If everything goes as planned your final effect should have the feeling and depth of  the actual stone lapis lazuli.  Keep in mind you can alter the shade of your stone by  adding more or less of a given pigment.