If you've ever cut lapis you'll have noticed the bright blue run off water and vivid sediment it produces - that stuff is precious, it used to be the most expensive pigment in the world - ultramarine. These days it's cheap and made synthetically but there are artists that will seek out the natural version and pay good money for it.
Straight off the rock it's not much good - it comes out very grey.
In renaissance times they'd have mixed the dust with a mix of beeswax, turpentine and mastic then mashed it water, releasing the pigment and leaving the other material trapped in the wax. It seems simple enough but mastic ain't exactly cheap so I started playing with other things.
I hit upon butter - I'm willing to bet any grease will do the job though.
I dried the lapis powder, then added the fat to form a dough - you'd be amazed how much you can work in. The plan was to squish the dough in cold water to release the pigment and leave me with a ball of crud to discard.
I was half right - I used a 2l jug with a litre of water, after five minutes I had a lot of blue water but the grease didn't stay in a lump - it coated my hands and the inside of the jug in grey sludge. That was probably an advantage - more surface area so faster extraction. No pics of this stage - I didn't dare touch anything, next time I'll have a couple of rags handy.
The ultramarine takes a while to sediment out so it's easy to pour off from the mess into a clean container, I threw some ice in to encourage any remaining butter to congeal and float to the top. For good measure I gave the pigment a wash in fresh water before drying it - in the end I got around 100g of ultramarine from 150g cutting waste. The last pic is a before and after of the stuff mixed with a bit of linseed.