Honestly, I would tell her that the stretchy velvet wouldn't work for the lap quilt and ask her to find a color/design of fabric in 100% cotton to replace the backing. I don't think the velvet would lay right and end up being loose in lot of places, especially once it is constantly used and washed. I would quilt the entire lap quilt once the new backing is on. The only other thing I can think of that might go with it, is a minky fabric or perhaps a light fleece (although fleece is also somewhat stretchy).