I do crazy quilts the same way my gran taught me - stitching scraps down to a square of muslin (or old sheet) then assembling the squares into a quilt.
Gran just used zigzags all over everything but I like to go back and add decorative stitches with my machine.
I love my crazy quilts and make about one a year. Great way to use up orphan blocks and lots of odd sized scraps. Mine are completely random and uncontrolled but I've seen some lovely ones where people sorted out colors. I do mine 100% on the machine.
I've never done one with lace but I have a bunch of vintage lace I've saved, along with a bunch of damaged table runners and dish towels that my grandmother embroidered, some of which have crocheted edges. Some day I'll assemble all of that into a crazy quilt designed to go up on a wall - most of it is stuff I don't think would survive a washing. That one I will probably hand-embroider any additional decorative stitching; I don't feel like machine decorative stitching would look right next to my gran's handwork.