After posting last night, I began to wonder about the authenticity of that gemstone. I didn't think to identify the stone prior to grinding it up. (I'm a gemologist in a prior life.) An indication of lazurite is a sensitivity to acids, so I sprinkled a pinch of pigment into white vinegar. Looks good as you can see in the photo; the blue within minutes disappeared. Still, it's only an indication. (By the way, no gemologist would ever conduct a destructive test without prior consent.)
Here's the pigment with linseed mixed with a palette knife.
I plan to pick up some natural untreated lapis chips and give this another try.