I looked up lapis on the web and read that most of the minerals are
an aluminum silicate. Potassium hydroxide will etch aluminum, but I
don't know how it will react when bonded to silica. It would only
take a minute to find out.
If the etch profile is isotropic, then you will need to consider
dimension limits on your monogram. If you are going to etch 0.020
inches deep, any dimension in your monogram that is less than 0.040
inches will likely disappear.
Mineral grain size will have an effect on the overall quality of the
line or edge. That you have a mix of different minerals makes the
etch process a lot less controllable.
Should I mention pinholes in your mask, or are you already reaching
for the diamond tools?