First, let me suggest that you reconsider. Rock is extremely hard to remove; when you try to sell your home, the amount of effort required to remove it could scare off potential buyers. If you must remove the lawn, consider using a bark mulch instead. It's better looking and easy to remove.
To answer your question, you can first spray the area with a non-selective weed killer such as RoundUp or AllDown (which is organic) to weaken or kill much of the turf.
Then cover the area with a breathable landscape fabric such as Typar -- get the thick kind designed to go under patios. Don't use the inexpensive woven landscape fabric sold at some big box home improvement stores.
Once the fabric is down, you're ready to cover it.
The fabric will last for several years, but will eventually begin to deteriorate. At that point, you might see weeds popping up here and there, which you can pull out.