We have a lawn at home, and we only water it on our water-restricted watering days (except very occasionally by hand if its a 40+ degree day). It keeps the garden cooler, and we assumed it was also a good carbon sink. Well, it is a good carbon sink, but it seems that all the grooming efforts eliminate that or worse: http://www.physorg.com/news183129874.html
I know that ours is only a garden lawn, and this study focussed on public parks, but some of the results must be transferrable – we mow our lawn and only a month or so ago we applied some fertiliser for the summer. We use an electric mower, so that probably helps as it is only drawing baseload from the power station (which is of the super-green, brown-coal-fired type!) – arguably better than an inefficient 2-stroke mower. But it calls into question the "greenness" of the backyard lawn, which does after all take up a considerable portion of the garden.
So, what do you do?
You could replace it with synthetic turf, but that would have all sorts of issues relating to its manufacture. Or you could replace it with gravel and the odd plant, but that would not have the cooling effect and would have even less carbon storage capacity. Perhaps its best to keep the lawn and not fertilise and mow less. Its a tricky area in a climate where everyone wants to do their bit.
As always with these issues, there is more than one aspect. Here we balance CO2 emissions against water security. Where we live, water is scarce and resources are stretched. Electricity generation produces tonnes of CO2. But it will be water that gets us first. Increasing population demands greater water supply. In an area at least 50% supplied by groundwater, much of which is "fossil water", it is obvious that a limit will be reached. What is worse, increasing water demand forces government to install desalination plants, further increasing electricity demand. A vicious cycle is established. SO, ultimately water demand reduction could have a double benefit – reduce the need to enhance supply and reduce expanding electricity demands.
Where does this leave the lawn? Well I guess it means replace it with a garden bed full of drought friendly plants that require little water. Either way, it reminds us that reducing water use is one of the best things you can do for the environment. Still, that lawn is a nice thing to have…