I agree with Russel, that it sounds like the original Wax Coating, and not paint.
Pictures would help us to identify the age, and let us see the surface more clearly.
Lye will remove some paint, not all, depending on the type of paint used.
I usually just hit a painted piece with Zip Strip to remove the paint, scrub down, and then into the lye bath, then electro.
My restoration regimen is so rigorous, that I have yet to worry about a lead test. Some folks buy the test kits at HD or Lowes or wherever else they are sold. I have always wondered though, if the isolated wipes with those small sticks are even effective.
My research tells me that the lye bath will convert/change the molecular structure of lead, and that would be left as residual in the lye bath.
:)