angierq, welcome to the CUTE family - I always use two layers of the mesh looking WSS (water soluable stabilizer) same thread in top and bobbin and a new needle, as debleerl suggested, as well. Make sure that the design that you are using is intened for FSL - some Lace designs are to be used on fabric. But FSL (free standing lace) is made to stand alone - once you rinse the WSS out - all that is left - is the thread.
Here's a link to a tutorial. Use 2 layers of the mesh type of water soluable stabilizer, not the clear kind shown in the video. Use the same thread on top and bottom. Use a new needle and slow down your machine. Welcome to the "Cute" family.
FSL is made without fabric. Unless the pattern specifically specifies that it is required. I just did a ballarina - she looks great. I use 2 layers Ultra Solvy which is 4 of regular or 8 or original. I am not sure if this right I learned from public TV. Also, I is a good idea to use the same color bobbin thread.