Well I came across the same problem as in the solar panels vs. green roof debate, that being finding stats on the CO2 absorption of grass. I did find one person who made a good point that often grass will die seasonally and release its stored carbon, but if you're keeping your grass perenially green (as Lance clearly is!), that's not the case.
In the debate, I found that a square meter of vetiver would absorb about 5 kg of CO2 during a year's growth. That's a big, deep-rooted grass, so I assumed more common grass would absorb half as much. I'll use the same assumption here.
So now let's say you're super cool and use a Neuton electric mower to mow your lawn. It uses 0.36 kWh to mow 1/3 acre, or 1350 square meters. That area of grass will absorb somewhere around 3,000 kg of CO2 over a year's growth. Let's say you mow your lawn every-other week, or 26 times anually. That's 9.36 kWh, which according to the EPA, corresponds to 12.76 lbs of CO2, or 5.8 kg. So you're golden.
According to Neuton (citing the EPA), a gas mower emits 87 lbs (39.5 kg) of CO2 per year. I don't know what assumptions they're making (stand-up or sit-down, mowing frequency, lawn size, etc.). But it's hard to find statistics on mower CO2 emissions, so we'll just call that an average, in which case lawns still do absorb a lot more CO2 than mowers emit. Of course, that's only if my assumptions about grass CO2 absorption are accurate, which may very well not be the case.