If you are going to line your corset, add the lace before you add the lining. Stitch the lace down with very small stitches showing on the outside, connected by longer stitches on the inside. Depending on the future of the garment, these inside stitches can be very long, even a few inches. Long stitches are more likely to snag, though, so that's best for clothes that will eventually be lined or that won't be worn often (sample garments, for example). If the garment needs to last longer and the stitching won't be covered, best to keep the float stitches between 1/2" - 1" (1 - 2cm). Basically, there's no wrong way to do it - as long as the applique stays on and doesn't sag, you're good.
Use a thread that blends well with the lace.