I'm guessing from your description that your lawn has probably largely reverted to less needy species. In which case, they don't need that maintenance to grow and you are probably beating that 8% pretty handily.
My front lawn right now is full of daisies. I have been purposely not mowing sections of it, because they're covered in bees and I can't bring myself to leave them nothing! Anyway, like you, I put in zero chemicals, but that stuff still grows well above 8% of the chemical-fed grass a few houses down.
I'd be curious to see data and analysis on lawn carbon footprint. For my lawn, everything I've been able to find suggests it is a negative carbon footprint.
I don't put any chemicals or fertilizer on it, so no carbon impact either way there.
I do not water it, so nothing either way there, either.
I do mow during the summer, with a gas powered push mower. The total gas used per year is under 1 gallon. Let's go with 1 gallon, although it is probably actually closer to around 0.6 or 0.7. A few different results on Google tell me that this will result in about 17 pounds or 8 kg of CO2 emission per year.
I haven't found much on how much CO2 a lawn can take out. What I have found was always about "well-managed" lawns, in a context where "well-managed" meant a lawn that is heavily watered, fertilized, and mowed. Those sequester almost 1000 pounds of carbon per acre per year. Note that was carbon, not CO2. That would be around 3400 pounds of CO2.
But you'd only get 3400 pounds of CO2 a year per acre if you are keeping the lawn constantly growing (hence the "well-managed" part), and the heavy watering, fertilizing, and mowing to do that will have have a high carbon cost.
My lot is about 1/5th acre, and my lawn only covers between 1/3 and 1/2 of it. Going with 1/3, then if my lawn were a "well-managed" (e.g., heavily watered, fertilized, mowed lawn), that would be about 230 pounds a year of CO2 reduction.
But it is not "well-managed", so I'm not getting maximum growth out of it. Still, as long as I'm getting at least around 8% of the growth a "well-managed" lawn would get, it looks like I'm coming out ahead, with the lawn sequestering more CO2 than the mowing produces.