Thanks to Marty S and anyone else who suggested MistyFuse. I actually found a fabric store not too far from me that carries it (in white only, but that will do!). I used it for my January piece and it works great!
My Lacey's got a bit thicker and it is now wavy on the back. I emailed the Lacey's folks and they told me that Lacey's is a polyester product, so I probably used too high a heat to fuse it. MistyFuse said to use the highest heat your fabric will allow, so I set my iron to cotton, the farbic I was attaching! I will try some experimenting with the iron set on polyester and see how the Lacey's fares and if the MistyFuse will stick.
MF is a great product, so thanks again!