(and considering the enormous amount of energy needed to pump that water from either the Colorado river, or from the Delta and over the grapevine, I doubt your grass is oxygen positive. Therefore, I think you are using MY oxygen. 😉 )
Actually that’s not the case. Here are some numbers.
Cost to pump fresh water to LA through California State Water Project: 3000 kwh/acre-foot or 9 wh/gallon
Carbon dioxide consumed by 1000 sf of grass: around 500-600 kg/year (hard to find good numbers)
Water spent to grow grass: let’s say 40″/year in addition to rainfall = 25,000 gallon/year = 225 kwh
worst-case scenario (100% coal-powered electricity): 1 kwh of electricity = 1 kg of emissions, 225 kwh = 225 kg
So, even in the worst-case scenario, my lawn would be net oxygen-positive. And California has fairly clean electricity.