Well, when it was time to get rid of mine, I would line the bottom of the truck with sod, then fill it up with dirt. When I'd get to the dump, I'd just refer to it as "fill."
I only got called on it once, and asked the person to show me where the city defines clean fill. They couldn't (I knew because I looked) and let me off with just the $5 clean fill dumping fee.
Bottom line is- make sure you know the cost and hassle of removing whatever it is that you are pulling up.
Another tip for Syl. Seeing as this lawn may have been killed by dog pee, go to Wal-Mart and look for the grass seed with the picture of a puppy on the front. Works wonders for lawns that have been destroyed by dogs.
I think the key is to make the lawn look like somebody will say "Give me one season and I'll have this lawn back into shape" as opposed to "why is the lawn dead."