repairing lawn

We have 3 lots, all about 1/4 acre each. Our home is one the lot to the north, the other 2 are to the south of us and are vacant. I mow everything weekly, the lots are full of trees, shrubs, etc.
Some idiot seems to have dumped cooking oil on one of the sections (I know who it is, but I can't speak spanish and they can't understand english). What's the easiest way to fix this? The grass seems to have died off. I am thinking of digging the affected area out, filling it back, and replanting. Then maybe exterminating the person who did this crap. :P

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