If I understand your quwstion rightly, you're asking about the empty space between solid parts?
If so, anything over 0.5mm should be ok, below that and you run the risk of areas being fused in the strong & flexible plastic.
What material are you inteding to have the lace dollie printed in?
For a negative space not to get printed as solid add a hole that attatchs the negative space to the outside of your model big enough so that the support material can be removed.
An enclosed negative area won't be recognized by shapeways and the product will be printed as solid. (In fud it can be enclosed i think but i'm not sure of that)If it doesn't look good it's not designed by us.