Hmmm - I've made several 2 layer lap-sized quilts with fleece backing instead of 3-layer quilts with regular batting, but it does require a lot more preparation and organization than a regular quilt because of the weight.
I pin the daylights out of it and machine quilt using my Pfaff's built in walking foot. Maybe the lap quilt size makes a difference, - 60inches maximum (the width of the fleece) by 50 inches up to 70 inches - helps.
The pins are no more than a closed fist apart. I don't do any fancy quilting, and I quilt at least every 4 inches to hold the thing together. I machine sew straight lines ONLY on these quilts. I do all the vertical lines first, and then the horizontal lines. I've used both 'thin' fleece and 'heavy' fleece. I just finished a heavy fleece one last week, and it turned out beautifully. I prefer thin fleece, but I had the heavier fleece in the house, and I didn't feel like shopping. . .
I don't wrestle with all that weight. I back my sewing table into a corner, so the weight of the quilt is not falling off the table in back of the sewing machine. I set up a card table beside my sewing table and an ironing board next to me to keep the weight of the quilt from dragging on the needle --- and ME.
I should have taken a picture while I was doing this., but I never think to do that, and I don't know how to upload it anyway. When I'm at my table arrrangement , I'm almost surrounded by the table, card table and ironing board almost like a 'dot' in the middle of a C. I hope that gives you the 'picture.'