Here's a very interesting set of posts on making paint from natural materials.
One of the colours she used was madder, which is particularly interesting in the light of my previous post about purple. In Thyatira, purple was made from the madder plant, not shellfish. This means it would be even redder than most ancient purple.
Interesting conundrum for illustrating: do I make Lydia's 'purple' completely historically accurate, therefore not actually what we would call purple at all? Or do I make it closer to what we would call purple - not being strictly accurate, but going as red as possible while still being purple to our eyes?
I think I would lean to the latter for illustrations to be used while telling a story. It has to make sense, and it's enough to have to stop and explain to the children that purple clothes were very expensive in those days, without trying to explain that they also weren't actually purple at all... In an information-type book, however, you could give more of an explanation.
Sometimes you need to use a wee bit of artists' license.