I've done many many lace jobs since I started working for others in the early seventies. I still have all of the how-to books I bought then! :-) I always just pulled it tight, then taped it good at the edges, and misted the paint on in light coats. That way you don't soak the lace, and glue it to the surface.
I also heard of some people dampening the lace to make it cling to the surface in dips and such.
I would be afraid of an adhesive, since you may have to clean up residue on fragile painted areas.
I won't bore you with flowered laces, but another thing I will mention is that you can buy abstract laces... halloween patterns like spider webs... patterns of palm leaves... random organic styles... and many many others. You can also use the plastic mesh bags from turkeys and onions etc. Those produce a reptilian pattern. I still use those non-flower fabrics occasionally to add texture and detail. Here are a small number of examples...