Lawn works best with other light weight fabrics, a lot of batiks for example are supple enough, but some of the thicker "quilting" cottons are best kept out of the project.
In some my of my early "wash" quilts where I was incorporating clothing scraps, I've had pieces of lawn that held up very well.
I also like lawn/lightweight backings and will sometimes use poly blends for a similar feel -- but when you are used to cotton slippery fabric can result in a bit of colorful language... I think I can count on about 10 years of heavy use and washing and yes, chances are the back will have to be replaced while the top is still worth a new back for another 10 years.
While I typically prefer a fluffier batting and less quilting than is currently popular, I would suggest quilting lawn down pretty securely for it to last the best.