These are all great pattern suggestions. (I've made notes :-)
To maximize the warmth of a lap throw (or any other size quilt), I highly recommend using fleece as the batting. While it's more expensive than other kinds of batting, it can (if you choose) eliminate the need for backing.
FWIW, using a coupon I can buy fleece at least a couple of times a year at my local "Mill End Textiles" for under $3/yard. While very few people want so much warmth, the elderly often do. I use it for their quilts.