Suppose one cut a piece of foam rubber so that the top would perfectly accomodate the body of a lute, and left the bottom flat so the entire assemblage (lute and foam rubber) would rest securely on the lap.
This would be bulky to carry around, but at least not heavy. It might eliminate the need for a strap or foot stool. And it does bear some resemblance to the historical idea of resting the lute against a table. Foam rubber is grippy, like those anti-skid cloths. To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html