This may seem obvious but even small amounts of water will keep the root systems alive. Allow the sun to do the baking. To expedite the heating process cover your lawn with heavy gauge plastic.
When the grass appears to be dead, remove the plastic and till the grass to about a 3 inch depth. This will then expose any grass roots that may be alive.
Cover the lawn again with the plastic and allow the exposed grass roots to bake and die. Repeat the till and bake process until the root system is totally destroyed.
To assure that no roots will remain to regenerate, rake the grass debris and discard. You can now replace your lawn with a number of alternative landscaping ideas.
Source: Local gardening program but I do not remember which one.
By Jenvieve from Austin, TX